Exhibit 10.4

ENTEROMEDICS INC.

CERTIFICATE OF DESIGNATIONS

FOR

SERIES A NON–VOTING CONVERTIBLE PREFERRED STOCK

(PURSUANT TO DELAWARE GENERAL CORPORATION LAW,

SECTION 151(G))

The undersigned, being the Chief Financial Officer, Vice President and Secretary of EnteroMedics Inc. (the “Corporation”), a corporation organized and existing under the Delaware General Corporation Law, in accordance with the provisions of the Delaware General Corporation Law, Section 151(g), do hereby certify that:

Pursuant to the authority vested in the Board of Directors of the Corporation by the Fifth Amended and Restated Certificate of Incorporation of the Corporation, the Board of Directors of the Corporation on September 9, 2010, in accordance with the Delaware General Corporation Law, Section 151, duly adopted the following resolution establishing a series of 3,600,000 shares of the Corporation’s Preferred Stock, to be designated as its Series A Non–Voting Convertible Preferred Stock:

RESOLVED, that pursuant to the authority vested in the Board of Directors of the Corporation (the “Board of Directors”) by the Fifth Amended and Restated Certificate of Incorporation of the Corporation, the Board of Directors hereby establishes a series of Series A Non–Voting Convertible Preferred Stock of the Corporation and hereby states the number of shares and fixes the powers, designations, preferences and relative, participating, optional and other rights, and the qualifications, limitations and restrictions thereof, of such series of shares as follows:

SERIES A NON–VOTING CONVERTIBLE PREFERRED STOCK

Section 1. Designation; Number of Shares. The shares of such series shall be designated as “Series A Non–Voting Convertible Preferred Stock” (the “Convertible Preferred Stock”), and the number of shares constituting the Convertible Preferred Stock shall be 3,600,000. Such number of shares may be decreased by resolution of the Board of Directors adopted and filed pursuant to the Delaware General Corporation Law, Section 151(g), or any successor provision; provided, that no such decrease shall reduce the number of authorized shares of Convertible Preferred Stock to a number less than the number of shares then outstanding plus the number of shares reserved for issuance upon the exercise of outstanding options, warrants, convertible or exchangeable securities or other rights to acquire shares of Convertible Preferred Stock.

Section 2. Stated Capital. The amount to be represented in the stated capital of the Corporation for each share of Convertible Preferred Stock shall be $0.01.

Section 3. Rank. The Convertible Preferred Stock shall rank prior to all of the Corporation’s Common Stock, par value $0.01 per share (the “Common Stock”), now outstanding or hereafter issued, as to distributions of assets upon the liquidation, dissolution or winding up of the Corporation, whether voluntary or involuntary.

Section 4. Dividends. So long as any shares of Convertible Preferred Stock remain outstanding, if the Corporation makes any dividend or distribution of cash, securities (including, but not limited to, rights, warrants, options or evidences of indebtedness) or properties or assets on shares of Common Stock, then the Corporation shall simultaneously declare and pay a dividend or distribution on shares of Convertible Preferred Stock in the amount of dividends or distributions that would be made with respect to shares of Convertible Preferred Stock if such shares were converted into shares of Common Stock on the record date for such dividend or distribution (or if no record date is established, at the date such dividend or distribution is declared).

Section 5. Liquidation Preference. In the event of a liquidation, dissolution or winding up of the Corporation, whether voluntary or involuntary, the holders of Convertible Preferred Stock shall be entitled to receive out of the assets of the Corporation, whether such assets constitute stated capital or surplus of any nature, an amount equal to the dividends accumulated and unpaid thereon to the date of final distribution to such holders, whether or not declared, without interest, plus a sum equal to $2.58 per share, and no more, before any payment shall be made or any assets distributed to the holders of Common Stock or any other capital stock of the Corporation ranking junior as to liquidation rights to the Convertible Preferred Stock (such Common Stock and other capital stock being referred to herein collectively as “Junior Liquidation Stock.” After payment in full of the liquidation preference of the shares of the Convertible Preferred Stock, the entire remaining assets and funds of the Corporation legally available for distribution, if any, shall be distributed among the holders of the Common Stock and the Convertible Preferred Stock in proportion to the shares of Common Stock then held by them and the shares of Common Stock which they then have the right to acquire upon conversion of the shares of Convertible Preferred Stock then held by them. A merger or consolidation (other than one in which stockholders of the Corporation own a majority by voting power of the outstanding shares of the surviving or acquiring corporation) and a sale, lease, transfer, exclusive license or other disposition of all or substantially all of the assets of the Corporation shall be deemed a liquidation, dissolution or winding up of the Corporation for purposes of this Section 5, thereby triggering payment of the liquidation preferences described above, unless the holders of 75% of the Convertible Preferred Stock elect otherwise.

Section 6. No Redemption. The shares of Convertible Preferred Stock shall not be redeemable.

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Section 7. Conversion.

(a) Conversion at Option of Holders.

(i) Subject to the limitation set forth in Section 7(e), holders of Convertible Preferred Stock may, at their option upon surrender of the certificates therefor, convert any or all of their shares of Convertible Preferred Stock into fully paid and nonassessable shares of Common Stock (and such other securities and property as they may be entitled to, as hereinafter provided) at any time after issuance thereof. Each share of Convertible Preferred Stock shall be convertible at the office of any transfer agent for the Convertible Preferred Stock, and at such other office or offices, if any, as the Board of Directors may designate, into that number of fully paid and nonassessable shares of Common Stock as shall be equal to the Conversion Rate, determined as hereinafter provided, in effect at the time of conversion. Shares of Convertible Preferred Stock may initially be converted into full shares of Common Stock as is determined by dividing (A) the Original Issue Price by (B) the sum of the Original Issue Price plus the Conversion Price, subject to adjustment from time to time as provided in Section 8 (such conversion rate, as so adjusted from time to time, being referred to herein as the “Conversion Rate”). “Original Issue Price” means $1.72. “Conversion Price” means $0.125 multiplied by the sum of the number of shares of Common Stock issuable under the converting holder’s Conversion Warrant (as defined in that certain Securities Purchase Agreement, dated as of the date hereof, between the Corporation and the investors purchasing Convertible Preferred Stock pursuant thereto (the “Securities Purchase Agreement”) divided by the number of Convertible Preferred Stock held by such converting holder. Upon conversion, no adjustment or payment shall be made in respect of accumulated and unpaid dividends on the Convertible Preferred Stock surrendered for conversion.

(ii) The right of holders of Convertible Preferred Stock to convert their shares shall be exercised by surrendering for such purpose to the Corporation or its agent, as provided above, certificates representing shares to be converted, duly endorsed in blank or accompanied by proper instruments of transfer. The Corporation shall not be required to pay any tax which may be payable in respect of any transfer involved in the issue and delivery of Common Stock or other securities or property upon conversion of Convertible Preferred Stock in a name other than that of the holder of the shares of Convertible Preferred Stock being converted, nor shall the Corporation shall be required to issue or deliver any such shares or other securities or property unless and until the person or persons requesting the issuance thereof shall have paid to the Corporation the amount of any such tax or shall have established to the satisfaction of the Corporation that such tax has been paid.

(b) Mandatory Conversion. Subject to the limitation set forth in Section 7(e), each share of Convertible Preferred Stock shall be automatically converted into shares of Common Stock at the then effective Conversion Rate (i) upon the date on which at least 75% of the outstanding shares of Convertible Preferred Stock elect such conversion or (ii) upon the closing of an offering of equity securities for the account of the Corporation (other than by sale of the Convertible Preferred Stock pursuant to the Securities Purchase Agreement), provided that the aggregate gross proceeds to the Corporation are $15 million or more (net of underwriting commissions and expenses) (an “Equity Offering”), provided further that the Convertible Preferred Stock shall not be deemed to have converted until immediately after the closing of the Equity Offering.

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(c) A number of shares of the authorized but unissued Common Stock sufficient to provide for the conversion of the Convertible Preferred Stock outstanding upon the basis hereinbefore provided shall at all times be reserved by the Corporation, free from preemptive rights, for such conversion, subject to the provisions of the next paragraph. If the Corporation shall issue any securities or make any change in its capital structure which would change the number of shares of Common Stock into which each share of the Convertible Preferred Stock shall be convertible as herein provided, the Corporation shall at the same time also make proper provision so that thereafter there shall be a sufficient number of shares of Common Stock authorized and reserved, free from preemptive rights, for conversion of the outstanding Convertible Preferred Stock on the new basis. The Corporation shall comply with all securities laws regulating the offer and delivery of shares of Common Stock upon conversion of the Convertible Preferred Stock.

(d) Upon the surrender of certificates representing shares of Convertible Preferred Stock to be converted, duly endorsed or accompanied by proper instruments of transfer as provided above, the person converting such shares shall be deemed to be the holder of record of the Common Stock issuable upon such conversion, and all rights with respect to the shares surrendered shall forthwith terminate except the right to receive the Common Stock or other securities, cash or other assets as herein provided.

(e) Notwithstanding any other provision of this Section 7, no stockholder of the Corporation’s capital stock shall be permitted to convert an amount of Convertible Preferred Stock that would result in such stockholder owning more than 19.99% of the Common Stock outstanding after such conversion.

Section 8. Adjustments to Conversion Rate.

(a) Notwithstanding anything in this Section 8 to the contrary, no change in the Conversion Rate shall be made until the cumulative effect of the adjustments called for by this Section 8 since the date of the last change in the Conversion Rate would change the Conversion Rate by more than 3%. However, once the cumulative effect would result in such a change, then the Conversion Rate shall be changed to reflect all adjustments called for by this Section 8 and not previously made. Subject to the foregoing, the Conversion Rate shall be adjusted from time to time as follows:

(i) In case the Corporation shall (A) pay a dividend or make a distribution on its Common Stock in shares of its capital stock, (B) subdivide its outstanding Common Stock into a greater number of shares, (C) combine the shares of its outstanding Common Stock into a smaller number of shares or (D) issue by reclassification of its Common Stock any shares of its capital stock, then in each such case the Conversion Rate in effect immediately prior thereto shall be proportionately adjusted so that the holder of any Convertible Preferred Stock thereafter surrendered for conversion shall be entitled to receive, to the extent permitted by applicable law, the number and kind of shares of capital stock of the Corporation which such holder would have owned or have been entitled to receive after the happening of such event had such Convertible Preferred Stock been converted immediately prior to the record date for such event (or if no record date is

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established in connection with such event, the effective date for such action). An adjustment pursuant to this subparagraph (a)(ii) shall become effective immediately after the record date in the case of a stock dividend or distribution and shall become effective immediately after the effective date in the case of a subdivision, combination or reclassification.

(b) Except as otherwise provided above in this Section 8, no adjustment in the Conversion Rate shall be made in respect of any conversion for share distributions or dividends theretofore declared and paid or payable on the Common Stock.

(c) Whenever the Conversion Rate is adjusted as herein provided, the Corporation shall send to each transfer agent for the Convertible Preferred Stock and the Common Stock, and to the NASDAQ Capital Market, a statement signed by the Chairman of the Board of Directors, the President or any Vice President of the Corporation and by its Treasurer or its Secretary stating the adjusted Conversion Rate determined as provided in this Section 8; and any adjustment so evidenced, given in good faith, shall be binding upon all stockholders and upon the Corporation. Whenever the Conversion Rate is adjusted, the Corporation shall give notice by mail at the time of, and together with, the next dividend payment to the holders of record of Convertible Preferred Stock, setting forth the adjustment and the new Conversion Rate and Conversion Price. Notwithstanding the foregoing notice provisions, failure by the Corporation to give such notice or a defect in such notice shall not affect the binding nature of such corporate action of the Corporation.

(d) Whenever the Corporation shall propose to take any of the actions specified in subparagraphs (a)(i) or (a)(ii) of this Section 8 which would result in any adjustment in the Conversion Rate, the Corporation shall cause a notice to be mailed at least 30 days prior to the date on which the books of the Corporation will close or on which a record will be taken for such action to the holders of record of the outstanding Convertible Preferred Stock on the date of such notice. Such notice shall specify the action proposed to be taken by the Corporation and the date as of which holders of record of the Common Stock shall participate in any such actions or be entitled to exchange their Common Stock for securities or other property, as the case may be. Failure by the Corporation to give such notice or any defect in such notice shall not affect the validity of the transaction.

Section 9. Convertible Preferred Stock Not Redeemable at Option of Holders or Exchangeable; No Sinking Fund. The Convertible Preferred Stock shall not be redeemable upon the request of holders thereof or exchangable for other capital stock or indebtedness of the Corporation or other property. The shares of Convertible Preferred Stock shall not be subject to the operation of a purchase, retirement or sinking fund.

Section 10. Voting Rights. The holders of Convertible Preferred Stock shall not have any voting rights except as set forth below in Section 11 or as otherwise from time to time required by law.

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Section 11. Certain Actions Not to be Taken Without Vote of Holders of Convertible Preferred Stock. So long as 10% of the shares of Convertible Preferred Stock are outstanding, in addition to any other vote or approval required under the Fifth Amended and Restated Certificate of Incorporation of the Corporation or the Amended and Restated Bylaws of the Corporation, the Corporation will not, without the written consent of the holders of at least 75% of the Convertible Preferred Stock, either directly or by amendment, merger, consolidation or otherwise (i) create or authorize the creation of or issue any other security convertible into or exercisable for any equity security, having rights, preferences or privileges senior to or on parity with the Convertible Preferred Stock, or increase the authorized number of shares of Convertible Preferred Stock or (ii) purchase or redeem or pay any dividend on any capital stock prior to the Convertible Preferred Stock other than stock repurchased from former employees or consultants in connection with the cessation of their employment or services, as the case may be, at the lower of fair market value or cost, other than as approved by the Board of Directors.

Section 12. Outstanding Shares. For purposes of this Certificate of Designations, all shares of Convertible Preferred Stock shall be deemed outstanding except for (a) shares of Convertible Preferred Stock held of record or beneficially by the Corporation or any subsidiary of the Corporation; (b) from the date of surrender of certificates representing Convertible Preferred Stock for conversion pursuant to Section 7, all shares of Convertible Preferred Stock which have been converted into Common Stock or other securities or property pursuant to Section 7.

IN WITNESS WHEREOF, the Corporation has caused this certificate to be signed by Gregory S. Lea, its Chief Financial Officer, Senior Vice President and Secretary, this 29th day of September, 2010.

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