Exhibit 99.1

FORM OF INSTRUCTIONS

AS TO USE OF

STEREOTAXIS, INC.

WARRANTS CERTIFICATES

CONSULT THE WARRANTS AGENT, YOUR BANK OR BROKER

AS TO ANY QUESTIONS

The following instructions relate to a warrants offering (the “Warrants Offering”) by Stereotaxis, Inc., a Delaware corporation (“Stereotaxis”), to the holders of record (the “Recordholders”) of its common stock, par value $0.001 per share (the “Common Stock”), as described in the accompanying Stereotaxis prospectus supplement dated September 4, 2015 (the “Prospectus”). Recordholders as of 5:00 p.m. New York City time on September 9, 2015 (the “Record Date”) are receiving, at no charge, transferable subscription warrants (the “Warrants”) to subscribe for and purchase shares of Common Stock (the “Underlying Shares”). In the Warrants Offering, Stereotaxis is offering an aggregate of up to 5,755,775 Underlying Shares.

Each Recordholder will receive a Warrant to purchase one share of common stock at a price of $1.10 per share (the “Subscription Price”) for every four shares of our Common Stock owned by such Recordholder as of 5:00 p.m., New York City time, on the Record Date (with the total number of Warrants issuable rounded down to avoid the issuance of fractional Warrants). The Warrants will expire if not exercised prior to 5:00 p.m., New York City time, on September 30, 2015, unless extended (the “Expiration Time”). No fractional Warrants will be distributed and no fractional shares will be issued. Any excess subscription payments received by the Warrants Agent will be returned, without interest, as soon as practicable. For example, if a holder of Warrants owned 125 shares of Common Stock as of 5:00 p.m., New York City time on the Record Date, it would receive 31 Warrants (rounded down from 31.25 Warrants) and would have the right to purchase 31 shares of Common Stock for the Subscription Price.

Each Warrants holder will be required to submit payment in full for all the shares it wishes to buy with its Warrants.

Stereotaxis will not be required to issue shares of Common Stock to you if the Warrants Agent does not receive your payment (whether delivered directly in the case you are a Recordholder or indirectly through a Recordholder in the case you are a beneficial owner but not a Recordholder) prior to the Expiration Time, regardless of when you send the subscription payment and related documents, unless you send the documents in compliance with the guaranteed delivery procedures described below. The period for exercising your Warrants may be extended by Stereotaxis in its sole discretion. If the expiration date of the Warrants Offering is so extended, Stereotaxis will give oral or written notice to the Warrants Agent on or before the scheduled expiration date and Stereotaxis will issue a press release announcing such extension no later than 9:00 a.m., New York City time, on the next business day after the most recently announced expiration of the Warrants Offering. Stereotaxis will extend the duration of the Warrants Offering as required by applicable law or regulation and may choose to extend it. Stereotaxis does not currently intend to extend the expiration of the Warrants Offering. To the extent that any completed subscription exercise documentation is received by the Warrants Agent after the expiration of the Warrants Offering, Stereotaxis may, in its sole discretion, choose to accept such subscription, but it shall be under no obligation to do so. The Warrants will be evidenced by transferable Warrants certificates (the “Warrants Certificates”).

Subject to the allocation described below, each Warrant also grants the holder an over-subscription privilege to purchase additional Underlying Shares that are not purchased by other Warrants holders pursuant to their Warrants, subject to potential purchase limits for Recordholders attempting to own 15% or more of the Common Stock of Stereotaxis. Each Warrants holder is entitled to exercise its over-subscription privilege only if it exercises its Warrants in full. If an insufficient number of Underlying Shares is available to fully satisfy all over-subscription requests, the available Underlying Shares will be distributed pro rata among Warrants holders who exercised their over-subscription privileges based on the number of Underlying Shares each Warrants holder subscribed for under its Warrants. If this pro rata allocation results in any Warrants holder receiving a greater number of Underlying Shares than the Warrants holder subscribed for pursuant to the exercise of the over-subscription privilege, then such Warrants holder will be allocated only that number of shares for which the Warrants holder over-subscribed, and the remaining Underlying Shares will be allocated among all other Warrants holders exercising the over-subscription privilege on the same pro rata basis described above. The proration process will be repeated until all Underlying Shares have been allocated or all over-subscription requests have been satisfied. No fractional shares will be issued pursuant to the over-subscription privilege and all prorations will be rounded down to eliminate subscriptions for fractional shares.

The number of Warrants to which you are entitled is printed on the face of your Warrants Certificate. You should indicate your wishes with regard to the exercise of your Warrants and over-subscription privilege by completing the appropriate portions of your Warrants Certificate and returning the certificate to the Warrants Agent in the envelope provided.

YOUR WARRANTS CERTIFICATES, OR NOTICE OF GUARANTEED DELIVERY, AND SUBSCRIPTION PRICE PAYMENT FOR EACH WARRANT THAT IS EXERCISED PURSUANT TO THE WARRANTS, INCLUDING FINAL CLEARANCE OF ANY CHECKS, MUST BE RECEIVED BY THE WARRANTS AGENT, ON OR BEFORE THE EXPIRATION TIME. ONCE A WARRANTS HOLDER HAS EXERCISED THE WARRANTS, SUCH EXERCISE MAY NOT BE REVOKED. WARRANTS NOT EXERCISED PRIOR TO THE EXPIRATION TIME OF THE WARRANTS OFFERING WILL EXPIRE.

1. Method of Subscription—Exercise of Warrants.

To exercise Warrants, complete your Warrants Certificate and send the properly completed and executed Warrants Certificate evidencing such Warrants with any signatures required to be guaranteed so guaranteed, together with payment in full of the Subscription Price for each Underlying Share subscribed for pursuant to the Warrants, to the Warrants Agent, on or prior to the Expiration Time. Payment of the aggregate Subscription Price will be held in a segregated account to be maintained by the Warrants Agent.

To exercise the over-subscription privilege, you should indicate the number of additional Underlying Shares that you would like to purchase in the space provided on your Warrants Certificate, as well as the number of shares of Common Stock that you beneficially own without giving effect to any Underlying Shares to be purchased in this Warrants Offering. When you send in your Warrants Certificate, you must also send the full Subscription Price in cash for the number of additional Underlying Shares that you have requested to purchase pursuant to the over-subscription privilege (in addition to the payment in cash due for Underlying Shares purchased through your Warrant).

All payments must be made in U.S. dollars for the full number of Underlying Shares being subscribed for (a) check or bank draft payable to Broadridge Corporate Issuer Solutions, Inc. upon a U.S. bank, (b) postal, telegraphic or express money order payable to the Warrants Agent, or (c) wire transfer of immediately available funds to accounts maintained by the Warrants Agent for purposes of accepting subscriptions in the Warrants Offering in accordance with the following account instructions (the “Subscription Account”):

Bank Name: U.S. Bank

ABA/Routing Number: 123000848

International/Swift Code: USBKUS44IMT

Address: 800 Nicollet Mall

Minneapolis, MN 55402 USA

Beneficiary Account Name: Broadridge

Account Number: 153910728465

FCC: Broadridge FBO Stereotaxis, Inc.

FFC: a/c 153910726998

Any wire transfer should clearly indicate the identity of the subscriber who is paying the Subscription Price by wire transfer. Payments will be deemed to have been received upon (i) clearance of any uncertified check, (ii) receipt by the Warrants Agent of any certified check or bank draft drawn upon a U.S. bank or of any postal, telegraphic or express money order or (iii) receipt of collected funds in the Subscription Account designated above. If paying by uncertified personal check, please note that the funds paid thereby may take five or more business days to clear. Accordingly, Warrants holders who wish to pay the aggregate Subscription Price by means of uncertified personal check are urged to make payment sufficiently in advance of the Expiration Time to ensure that such payment is received and clears by such date and are urged to consider payment by means of certified or cashier’s check, money order or wire transfer of funds.

The Warrants Certificate and payment of the aggregate Subscription Price if by check or bank draft drawn upon a U.S. bank or postal, telegraphic or express money order, or, if applicable, Notices of Guaranteed Delivery (as defined below) must be delivered to the Warrants Agent by hand delivery, first class mail or courier service to:

By hand or overnight courier:

Broadridge Corporate Issuer Solutions, Inc.

Attn: BCIS IWS

51 Mercedes Way

Edgewood, NY 11717

By mail:*

Broadridge Corporate Issuer Solutions, Inc.

Attn: Re-Organization Dept., P.O. Box 1317

Brentwood, NY 11717.

Delivery to an address other than the applicable address above does not constitute valid delivery.

If you have any questions, require assistance regarding the method of exercising Warrants or require additional copies of relevant documents, please contact the Warrants Agent, Broadridge Corporate Issuer Solutions, Inc. at (855) 300-4994.

By making arrangements with your bank or broker for the delivery of funds on your behalf, you may also request such bank or broker to exercise the Warrants Certificate on your behalf. Alternatively, you may cause a written guarantee, a copy of which is being furnished to you (the “Notice of Guaranteed Delivery”), from a member firm of a registered national securities exchange or a member of the Financial Industry Regulatory Authority, or from a commercial bank or trust company having an office or correspondent in the United States or from a bank, shareholder, savings and loan association or credit union with membership in an approved signature guarantee medallion program, pursuant to Rule 17Ad-15 of the Securities Exchange Act of 1934, as amended, (each, an “Eligible Institution”), to be received by the Warrants Agent on or prior to the Expiration Time together with payment in full of the applicable Subscription Price. Such Notice of Guaranteed Delivery must state your name, the number of Warrants represented by the Warrants Certificate or Warrants Certificates held by you, the number of Underlying Shares being subscribed for pursuant to the Warrants and that you will guarantee the delivery to the Warrants Agent of any properly completed and executed Warrants Certificate or Warrants Certificates evidencing such Warrants within three (3) business days following the date of the Notice of Guaranteed Delivery. If this procedure is followed, the properly completed Warrants Certificate or Warrants Certificates evidencing the Warrant or Warrants being exercised, with any signatures required to be guaranteed so guaranteed, must be received by the Warrants Agent within three (3) business days following the date of the Notice of Guaranteed Delivery. The Notice of Guaranteed Delivery may be delivered to the Warrants Agent in the same manner as Warrants Certificates at the address set forth above. Additional copies of the Notice of Guaranteed Delivery may be obtained upon request from the Warrants Agent at the address set forth above, or by calling the Warrants Agent at (855) 300-4994. In connection with the exercise of the over-subscription privilege, banks, brokers and other nominee holders of Warrants who act on behalf of beneficial owners will be required to certify as to the aggregate number of Warrants exercised, and the number of Underlying Shares requested through the over-subscription privilege, by each beneficial owner on whose behalf the nominee holder is acting.

If you do not indicate the number of Warrants being exercised, or do not forward full payment of the Subscription Price, then you will be deemed to have exercised first your Warrants with respect to the maximum number of whole Warrants that may be exercised with the aggregate Subscription Price you delivered to the Warrants Agent and the payment received will thereafter be applied, to the fullest extent possible based on the amount of excess payment received, to exercise your over-subscription privilege, if applicable, subject to the availability of Underlying Shares.

If Stereotaxis does not apply your full Subscription Price payment to your purchase of shares of Common Stock, the excess subscription payment received by the Warrants Agent will be returned to you, without interest, as soon as practicable.

2. Issuance of Common Stock.

The following deliveries and payments will be made to the address shown on the face of your Warrants Certificate, unless you provide instructions to the contrary in your Warrants Certificate.

(a) Warrants. As soon as practicable after the closing of the Warrants Offering and the valid exercise of Warrants, the Warrants Agent will mail to each Warrants holder that validly exercises the Warrants (and any over-subscription privilege) certificates representing shares of Common Stock purchased pursuant to the Warrants.

(b) Excess Cash Payments. As soon as practicable after the Expiration Time, any excess subscription payments received in payment of the Subscription Price by the Warrants Agent will be mailed to each Warrants holder, without interest.

3. Sale or Transfer of Warrants.

The Warrants granted to you will be transferable during the course of the Warrants Offering, and the Warrants are listed on the Nasdaq Capital Market under the symbol “STXSW”. As a result, you may transfer or sell your Warrants if you do not want to purchase any shares of our Common Stock. If you purchase Warrants in the open market or otherwise, and the Warrants Offering is not completed, the purchase price paid for such Warrants will not be returned to you.

4. Execution.

(a) Execution by Registered Holder. The signature on the Warrants Certificate must correspond with the name of the registered holder exactly as it appears on the face of the Warrants Certificate without any alteration or change whatsoever. Persons who sign the Warrants Certificate in a representative or other fiduciary capacity must indicate their capacity when signing and, unless waived by the Warrants Agent in its sole and absolute discretion, must present to the Warrants Agent satisfactory evidence of their authority to so act.

(b) Execution by Person Other than Registered Holder. If the Warrants Certificate is executed by a person other than the holder named on the face of the Warrants Certificate, proper evidence of authority of the person executing the Warrants Certificate must accompany the same unless, for good cause, the Warrants Agent dispenses with proof of authority.

(c) Signature Guarantees. Your signature must be guaranteed by an Eligible Institution (as defined above) if you specify special delivery instructions. See the “Form of Election to Purchase” attached to your Warrants Certificate(s).

5. Method of Delivery.

The method of delivery of Warrants Certificates and payment of the aggregate Subscription Price to the Warrants Agent will be at the election and risk of the Warrants holder. However, if you elect to exercise your Warrants, Stereotaxis urges you to consider using a certified or cashier’s check, money order, or wire transfer of funds to ensure that the Warrants Agent receives your funds prior to the Expiration Time. If you send an uncertificated check, payment will not be deemed to have been received by the Warrants Agent until the check has cleared, but if you send a certified check, bank draft drawn upon a U.S. bank, a postal, telegraphic or express money order or wire or transfer funds directly to the Warrants Agent’s account, payment will be deemed to have been received by the Warrants Agent immediately upon receipt of such instruments and wire or transfer. Any personal check used to pay for shares of Common Stock must clear the appropriate financial institutions prior to the Expiration Time. The clearinghouse may require five or more business days. Accordingly, Warrants holders that wish to pay the aggregate Subscription Price by means of an uncertified personal check are urged to make payment sufficiently in advance of the Expiration Time to ensure such payment is received and clears by such date.

6. Special Provisions Relating to the Delivery of Warrants through the Depository Trust Company.

In the case of Warrants that are held of record through The Depository Trust Company (“DTC”), exercises of the Warrants may be effected by instructing DTC to transfer Warrants from the DTC account of such holder to the DTC account of the Warrants Agent, together with certification as to the aggregate number of Warrants exercised subscribed for pursuant to the Warrants by each beneficial owner of Warrants on whose behalf such nominee is acting, and payment to the Warrants Agent of the Subscription Price for each share of Common Stock subscribed for pursuant to the Warrants. See the Company’s “Letter to Shareholders” and “Form of Election to Purchase” attached to your Warrants Certificate(s).

7. Substitute Form W-9.

TO ENSURE COMPLIANCE WITH IRS CIRCULAR 230, YOU ARE HEREBY NOTIFIED THAT: (A) ANY DISCUSSION OF U.S. FEDERAL TAX ISSUES CONTAINED OR REFERRED TO HEREIN IS NOT INTENDED OR WRITTEN TO BE USED, AND CANNOT BE USED BY ANY TAXPAYER FOR THE PURPOSE OF AVOIDING U.S. FEDERAL, STATE OR LOCAL TAX PENALTIES, (B) SUCH DISCUSSION IS WRITTEN IN CONNECTION WITH THE PROMOTION OR MARKETING OF THE TRANSACTION OR MATTERS DISCUSSED HEREIN, AND (C) THE TAXPAYER SHOULD SEEK ADVICE BASED ON THEIR PARTICULAR CIRCUMSTANCES FROM AN INDEPENDENT TAX ADVISOR.

Each Warrants holder who elects to exercise Warrants should provide the Warrants Agent with a correct Taxpayer Identification Number (“TIN”) on Substitute Form W-9, a copy of which is being furnished to each Warrants holder. Additional copies of Substitute Form W-9 may be obtained upon request from the Warrants Agent at the address set forth above or by calling the Warrants Agent at (855) 300-4994. Failure to provide the information on the form may subject such holder to a $50.00 penalty for each such failure and to U.S. federal income tax backup withholding (currently at a 28% rate) with respect to dividends that may be paid by Stereotaxis on shares of Common Stock purchased upon the exercise of Warrants (for those holders exercising Warrants).

8. Determinations Regarding the Exercise of Your Warrants.

Stereotaxis will decide, in its sole discretion, all questions concerning the timeliness, validity, form, and eligibility of the exercise of your Warrants. Any such determinations by Stereotaxis will be final and binding. Stereotaxis, in its sole discretion, may waive, in any particular instance, any defect or irregularity or permit, in any particular instance, a defect or irregularity to be corrected within such time as Stereotaxis may determine. Stereotaxis will not be required to make uniform determinations in all cases. Stereotaxis may reject the exercise of any of your Warrants because of any defect or irregularity. Stereotaxis will not accept any exercise of Warrants until all irregularities have been waived by Stereotaxis or cured by you within such time as Stereotaxis decides, in its sole discretion.

Neither Stereotaxis nor the Warrants Agent will be under any duty to notify you of any defect or irregularity in connection with your submission of Warrants Certificates, and Stereotaxis will not be liable for failure to notify you of any defect or irregularity. Stereotaxis reserves the right to reject your exercise of Warrants if Stereotaxis determines that your exercise is not in accordance with the terms of the Warrants Offering, as set forth in the Prospectus and these Instructions for Use, or in proper form. Stereotaxis will also not accept the exercise of your Warrants if Stereotaxis’s issuance of shares of Common Stock to you could be deemed unlawful under applicable law.

Stereotaxis reserves the right to reject any over-subscription requests and will, in most cases, reject an over-subscription request to the extent the Recordholder together with its affiliates would own 15% or more of the Common Stock of Stereotaxis after the over-subscription privilege is exercised. If Stereotaxis rejects any over-subscription requests, then such person will be allocated only that number of Underlying Shares for which the person is permitted to purchase, and the remaining Underlying Shares will be allocated among all other persons exercising the over-subscription privilege on the same basis described above. The allocation process will be repeated until all Underlying Shares have been allocated or all over-subscription requests have been satisfied, whichever occurs first.