Exhibit 99.1

WARRANT PURCHASE AGREEMENT

THIS WARRANT PURCHASE AGREEMENT (this “Agreement”) is made and entered into as of February 28, 2011, by and between Robert A. Spass (the “Seller”) and Endurance Specialty Holdings Ltd., an exempted company organized in Bermuda (the “Company”).

WHEREAS, the Seller desires to sell to the Company, and the Company desires to purchase from the Seller, warrants exercisable for 90,000 ordinary shares, par value US$1.00 per share (“Ordinary Shares”), of the Company having an exercise price as of the date hereof of $12.87 per Ordinary Share (the “Warrants”), and subject to the terms, conditions, promises, representations and warranties set forth herein; and

WHEREAS, the parties hereto desire to set forth herein the terms and conditions of their agreements and understandings.

NOW, THEREFORE, in consideration of the foregoing, of the mutual promises herein contained and of other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound, hereby covenant and agree as follows:

1. Sale and Transfer of the Warrants. The Seller hereby sells, assigns, transfers, conveys and delivers the Warrants to the Company.

2. Instruments of Conveyance and Transfer. As of the Closing (as defined herein), the Seller (i) will deliver to the Company an assignment separate from certificate for Warrant Number 111 currently held in book entry by the Company in such form satisfactory to the Company as shall be effective to vest in the Company good and valid title to the Warrants, free and clear of any option, call, contract, commitment, demand, lien, charge, security interest or encumbrance whatsoever and (ii) instructs the Company to issue a new warrant to be held in book entry by the Company for the purchase of the remaining 253,892 Ordinary Shares not being purchased from the Company and currently represented by Warrant Number 111. The Seller shall at any time, and from time to time, after the date hereof, execute, acknowledge and deliver all further assignments, transfers, and any other such instruments of conveyance, upon the request of the Company, to confirm the sale of the Warrants hereunder.

3. Payment by Buyer. At Closing, the Company is purchasing the Warrants at a purchase price of US$36.72 per Warrant, or an aggregate total purchase price of US$3,304,800 (the “Purchase Price”), by wire transfer of immediately available funds.

4. Closing. The transactions contemplated herein shall close on March 1, 2011 (the “Closing”), at which time, upon delivery by the Seller of such documents as required pursuant to Section 2 hereof, the Company shall deliver the Purchase Price by wire transfer of immediately available funds to such account or accounts as provided in writing to the Company by the Seller.

5. Representations and Warranties of Seller. As of the date hereof and the date of the Closing, the Seller represents and warrants that:

(a) The Seller has the full, absolute and entire power and legal right to execute, deliver and perform this Agreement.

(b) When duly and validly executed, this Agreement will constitute a legal, valid and binding obligation of the Seller enforceable against the Seller in accordance with its terms.

(c) The Warrants are owned of record and beneficially by Seller, free and clear of any option, call, contract, commitment, demand, lien, charge, security interest or encumbrance whatsoever.

6. Representations and Warranties of the Company. As of the date hereof and the date of the Closing, the Company represents and warrants that:

(a) The Company has the full, absolute and entire power and legal right to execute, deliver and perform this Agreement.

(b) The execution and delivery by the Company of this Agreement and the consummation of the transactions contemplated hereby have been duly and validly authorized by all necessary action on part of the Company and when duly and validly executed, will constitute a legal, valid and binding obligation of the Company enforceable against the Company in accordance with its terms.

7. Acknowledgments. As of the date hereof and the date of the Closing, the Seller acknowledges that:

(a) The Seller has not relied upon any representations (whether oral or written) with respect to the Company or the Warrants other than as set forth in this Agreement.

(b) The Seller has had an opportunity to discuss the Company’s business, management and financial affairs with directors, officers and management of the Company. The Seller has also had the opportunity to ask questions of and receive answers from, the Company and its management regarding the terms of this transaction. The Seller believes that he has received all the information he considers necessary or appropriate for deciding whether to sell the Warrants and has made his own analysis and decision to sell the Warrants to the Company based upon such information as the Seller deems appropriate.

(c) The Seller represents that he (i) is an “accredited investor” as that term is defined in Regulation D promulgated under the Securities Act of 1933, as amended (“Regulation D”) and has such knowledge, sophistication and experience in financial and business matters as to be capable of evaluating independently the merits, risks and suitability of entering into this Agreement and the transactions contemplated hereby, (ii) is able to bear the risks attendant to the transactions contemplated hereby, and (iii) is dealing with the Company on a professional arm’s-length basis as defined in Regulation D.

(d) The Seller acknowledges and agrees that he has had a full and complete opportunity to consult legal, tax and business advisors and has in fact consulted such advisors with respect to this agreement and any matters contemplated hereunder. The Seller further acknowledges that he has not engaged or employed any broker or finder in connection with the transactions referred to herein and that the sale of the Warrants has been privately negotiated by the Seller and the Company.

8. Governing Law. This Agreement shall be construed in accordance with the laws of Bermuda.

9. Invalidity or Unenforceability. In case any one or more of the provisions contained in this Agreement shall, for any reason, be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not affect the other provisions of this Agreement, and this Agreement shall be construed as if such invalid, illegal or unenforceable provision had never been contained herein.

10. Benefits and Burdens. This Agreement is binding upon, and inures to the benefit of, the parties hereto and their respective estates, executors, administrators, legatees, heirs, and personal and legal representatives, successors and permitted assigns.

11. Change; Waiver. No change or modification of this Agreement shall be valid unless the same is in writing and signed by the parties hereto. No waiver of any provision of this Agreement shall be valid unless in writing and signed by the party waiving its or his rights. The failure of either party at any time to insist upon, or any delay by either party at any time to insist upon, strict performance of any condition, promise, agreement or understanding set forth herein shall not be construed as a waiver or relinquishment of the right to insist upon strict performance of the same condition, promise, agreement or understanding at a future time.

12. Entire Agreement. This Agreement sets forth all of the promises, agreement, conditions, understandings and covenants between the parties hereto with respect to the subject matter referred to herein, and there are no promises other than as set forth herein. Any and all prior agreements with respect to such subject matter are hereby revoked. This Agreement is, and is intended by the parties to be, an integration of any and all prior agreements or understandings, oral or written, with respect to such subject matter.

13. Headings. The headings and other captions in this Agreement are for convenience and reference only and shall not be used in interpreting, construing or enforcing any of the provisions of this Agreement.

14. Counterparts. This Agreement may be executed in any number of counterparts, which may be by facsimile, all of which counterparts taken together shall constitute one and the same instrument.

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first above written.