Exhibit 10.2

Restricted Share Agreement

This RESTRICTED SHARE AGREEMENT (this “Agreement”) is made by and between Endurance Specialty Holdings Ltd., an exempted company organized under the laws of Bermuda (the “Company”) and John R. Charman (the “Executive”), as of May 28, 2013.

WHEREAS, the Executive is to become the Chairman and Chief Executive Officer of the Company, and the Company desires to increase the incentive of the Executive to exert his utmost efforts to improve the business and increase the assets of the Company; and

WHEREAS, as a material inducement to the Executive’s agreeing to accept employment with the Company, the Company wishes to grant the Executive this restricted share award set forth in this Agreement in accordance with the employment inducement award exception set forth in Section 303A.08 of the New York Stock Exchange Listed Company Manual.

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. Definitions. Capitalized terms used and not defined in this Agreement shall have the respective meanings ascribed to such terms in the Employment Agreement, dated May 28, 2013, between the Company and the Executive, as amended from time to time (the “Employment Agreement’). In addition to the foregoing, the following definitions shall be applicable within this Agreement.

a. “Restricted Period” means the period from the date of this Agreement to the applicable date of release of the restrictions set forth in this Agreement in accordance with the schedule set forth in Section 4 or earlier in accordance with Section 6.

b. “Shareholder Agreement” means the Shareholder Agreement, dated May 28, 2013, among the Company, Dragon Global Holdings Limited and the Executive, as amended from time to time.

2. Grant of Restricted Stock. The Company hereby grants to the Executive 708,890 shares (the “Restricted Shares”) of the Company’s ordinary shares, par value $1.00 per share (the “Ordinary Shares”), pursuant to and subject to the terms and provisions set forth in this Agreement. The Restricted Shares shall be issued and registered in the name of the Executive credited as fully-paid on the date of this Agreement. The Company will deliver to the Executive a copy of its register of shareholders evidencing the registration of the Restricted Shares in the name of the Executive.

3. Escrow of Restricted Shares. To insure the availability for delivery of the Executive’s Restricted Shares, the Executive hereby appoints the Secretary of the Company, or any other person designated by the Board of Directors of the Company (the

“Board”) as escrow agent, as his attorney-in-fact to assign and transfer unto the Company such Restricted Shares, if any, forfeited by the Executive pursuant to Section 6 below and shall, upon execution of this Agreement, deliver and deposit with the Secretary of the Company, or such other person designated by the Board, the certificates representing the Restricted Shares, together with the stock assignment duly endorsed in blank, attached hereto as Exhibit A, whether the Restricted Shares are held in certificated form or in book entry.

The share certificates representing the Restricted Shares and stock assignment shall be held by the Secretary in escrow, pursuant to the Joint Escrow Instructions of the Company and the Executive attached hereto as Exhibit B, until the Restricted Period has lapsed with respect to the Restricted Shares, or until such time as this Agreement no longer is in effect. Upon such time as the Restricted Period has with respect to any Restricted Shares lapsed pursuant to the schedule set forth in Section 4 below and subject to the forfeiture and Restricted Period termination provisions of Section 6 below, the escrow agent shall promptly deliver to the Executive the share certificates representing those Restricted Shares in the escrow agent’s possession belonging to the Executive in accordance with the terms of the Joint Escrow Instructions, either in certificated or book entry form, and the escrow agent shall be discharged of all further obligations hereunder.

4. Restrictions and Restricted Period.

a. Restrictions. Restricted Shares granted hereunder may not be sold, assigned, transferred, pledged, hypothecated or otherwise disposed of by the Executive except following the release of the restrictions in accordance with the schedule set forth in this Section or in accordance with Section 6. Restricted Shares granted hereunder are subject to a risk of forfeiture as described in Section 6 below until the release of the restrictions in accordance with the schedule set forth in this Section or in accordance with Section 6.

b. Restricted Period. Subject to Section 6, the restrictions set forth above shall lapse and the Restricted Shares shall become fully and freely transferable (provided, that such transfer is otherwise in accordance with the Shareholder Agreement and applicable law) and non-forfeitable on the dates and in the amounts as set forth below:

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5. Rights of a Shareholder. From and after the date of this Agreement and for so long as the Restricted Shares are held by the Executive, the Executive shall have all the rights of a shareholder of the Company with respect to the Restricted Shares, including, but not limited to, the right to receive dividends and the right to vote such Restricted Shares.

6. Forfeiture of Restricted Shares.

a. General. In the event the Executive’s employment with the Company is terminated (i) by the Company for Cause or (ii) by the Executive without Good Reason, the Restricted Shares (and any and all accrued but unpaid dividends in respect of those shares) that have not been released from the restrictions under Section 4 as of the Date of Separation from Service, shall be forfeited to the Company without payment of any consideration by the Company, and neither the Executive nor any of his successors, heirs, assigns, or personal representatives shall thereafter have any further rights or interests in such Restricted Shares or certificates representing those Restricted Shares.

b. Death or Disability.

i. In the event the Executive’s employment with the Company is severed as a result of the Executive’s death or Disability, the restrictions on 50 percent of the unvested Restricted Shares that remain subject to restrictions under Section 4 as of the Executive’s Date of Separation from Service due to death or Disability shall be released and such Restricted Shares shall become fully and freely transferrable and non-forfeitable on such Date of Separation from Service.

ii. In the event the Executive shall die or become subject to a Disability within 30 days of the Executive’s Date of Separation from Service as a result of the Executive severing his employment with the Company without Good Reason, the restrictions on 50 percent of the unvested Restricted Shares that remain subject to restrictions under Section 4 as of the Executive’s death or Disability shall be released and such Restricted Shares shall become fully and freely transferrable and non-forfeitable on the date of the Executive’s death or Disability as the case may be.

c. Termination of the Executive without Cause or by the Executive with Good Reason other than During a Change in Control Period. In the event of a termination by the Company of the Executive’s employment with the Company other than during a Change in Control Period by the Company without Cause or by the Executive with Good Reason, the restrictions on 50 percent of the unvested Restricted Shares that remain subject to restrictions under Section 4 as of the Executive’s Date of Separation from Service without Cause or for Good Reason shall be released and such Restricted Shares shall become fully and freely transferrable and non-forfeitable on such Date of Separation from Service.

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d. Termination of the Executive without Cause or by the Executive with Good Reason During a Change in Control Period. In the event of a Change in Control and the termination by the Company of the Executive’s employment with the Company during a Change in Control Period by the Company without Cause or by the Executive with Good Reason, the restrictions on all Restricted Shares shall be released and such Restricted Shares shall become fully and freely transferrable and non-forfeitable as of the Executive’s Date of Separation from Service.

7. Repayment or Forfeiture. Any benefits the Executive may receive hereunder may be subject to repayment or forfeiture as may be required in order to comply with the requirements of the U.S. Securities and Exchange Commission or any applicable law, including the requirements of the Dodd-Frank Wall Street Reform and Consumer Protection Act, or any securities exchange on which the Ordinary Shares are traded, as may be in effect from time to time.

8. Certificates. The Restricted Shares granted herein may be evidenced in such manner as the Board shall determine. If certificates representing the Restricted Shares are registered in the name of the Executive, then the Company shall retain physical possession of the certificates representing shares which remain subject to restrictions under section 4.

9. Legends. All certificates representing any of the Restricted Shares subject to the provisions of this Agreement shall have endorsed thereon the following legend:

“The transferability of this certificate and the ordinary shares represented hereby are subject to the restrictions, terms and conditions (including forfeiture provisions and restrictions against transfer) contained in a Shareholder Agreement and a Restricted Share Agreement entered into between the registered owner of such ordinary shares and the Company.”

10. Tax Withholding.

a. Subject to Section 10(b), it shall be a condition to the obligation of the Company to issue Ordinary Shares to the Executive upon the lapse of restrictions on the Restricted Shares that the Executive pay to the Company, upon demand (but no later than 10 days following such demand), such amount as may be requested by the Company for the purpose of satisfying any liability to withhold income or other taxes. In the event any such amount so requested is not paid, the Company may refuse to issue Ordinary Shares to the Executive upon the lapse of restrictions on the Restricted Shares. Unless the Board shall in its discretion determine otherwise, payment for taxes required to be withheld may be made in cash, or in whole or in part, in accordance with such rules as may be adopted by the Board from time to time, (i) by withholding Restricted Shares having a fair market value less than or equal to the required tax withholding liability and/or (ii) tendering to the Company Ordinary Shares held by the Executive having a fair market value less than or equal to the required tax withholding liability, in each case as determined by the Company in its sole discretion.

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b. Section 10(a) shall not apply in respect of any taxes in respect of the Restricted Shares which arise in Bermuda or in any jurisdiction outside Bermuda, where the tax liability outside Bermuda arises as a result of a requirement of the Company that the Executive provides services to the Company and its subsidiaries and affiliates outside Bermuda. The Company shall be responsible for and will duly and promptly report for and pay any payroll taxes in respect of the Restricted Shares which arise in Bermuda .

11. Termination of this Agreement. This Agreement shall terminate upon the earliest to occur of (a) the termination of the Restricted Period with respect to all of the Restricted Shares in accordance with Section 4 of this Agreement, (b) the forfeiture of Restricted Shares or early termination of the Restricted Period in accordance with Section 6 of this Agreement, (c) the termination of this Agreement by an instrument in writing signed by the parties hereto or (d) as may be required under applicable law. Upon termination of this Agreement, all rights and obligations of the Executive and the Company hereunder shall cease.

12. Agreement to Perform Necessary Acts. Each party to this Agreement agrees to perform any further acts and execute and deliver any documents that may be reasonably necessary to carry out the provisions of this Agreement.

13. Registration of Shares. The Company shall use commercially reasonable efforts to file and maintain an effective Registration Statement on Form S-8 under the United States Securities Act of 1933, as amended, with respect to the resale of the Restricted Shares.

14. No Limitation on Rights of the Company. This Agreement shall not in any way affect the right or power of the Company to make adjustments, reclassifications or changes in its capital or business structure or to merge, consolidate, dissolve, liquidate, sell or transfer all or any part of its business or assets.

15. Miscellaneous.

a. Notices. Any notice or other communication required or permitted hereunder shall be in writing and shall be delivered personally or sent by certified, registered, or express mail, postage prepaid. Any such notice shall be deemed given when delivered to each party at the following addresses (or to such other address as may be designated in a notice given in accordance with this Section):

(i) if to the Company:

Endurance Specialty Holdings Ltd.

Wellesley House

90 Pitts Bay Road

Pembroke HM 08

Bermuda

Attn: General Counsel

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(ii) if to the Executive, to the most recent primary residence address listed for the Executive in the employment records of the Company.

b. Failure to Enforce Not a Waiver. The failure of the Company or the Executive to enforce at any time any provision of this Agreement shall in no way be construed to be a waiver of such provision or of any other provision hereof.

c. Governing Law. This Agreement shall be governed by and construed according to the laws of Bermuda without giving effect to the choice of law principles thereof. The Executive submits (subject to Section 15(d)) to the non-exclusive jurisdiction of the courts of Bermuda in respect to matters arising hereunder.

d. Arbitration. All disputes, controversies or claims arising out of, relating to or in connection with this Agreement or the Restricted Shares, or the breach, termination or validity thereof, shall be finally settled by arbitration. The arbitration shall be conducted in accordance with the arbitration procedures set forth in Section 7.7 of the Employment Agreement.

e. Amendments. This Agreement may be amended or modified at any time by an instrument in writing signed by the parties hereto.

f. Investment Intent. Recipient represents that the Restricted Shares are being acquired by him for investment and that he has no present intention to transfer, sell or otherwise dispose of the Restricted Shares, except in compliance with applicable securities laws, and the parties agree that the Restricted Shares are being acquired in accordance with and subject to the terms, provisions and conditions of this Agreement.

g. Adjustment of Restricted Shares. The Company hereby confirms that (i) in the event the outstanding Ordinary Shares of the Company shall be changed into an increased number of shares, through a share dividend or bonus issue or a split-up of shares, or into a decreased number of shares, through a combination of shares, then immediately after the record date for such change, the number of Restricted Shares shall be proportionately increased, in case of such stock dividend or bonus issue or split-up of shares, or proportionately decreased, in case of such combination of shares; and (ii) in the event that, as result of a reorganization, sale, merger, amalgamation, consolidation or similar occurrence, there shall be any other change in the Ordinary Shares of the Company, or of any shares or other securities into which such Ordinary Shares shall have been changed, or for which they shall have been exchanged, then equitable adjustments to the Restricted Shares (including, but not limited to, changes in the number or kind of shares) shall be made.

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h. Agreement Not a Contract of Employment. This Agreement is not a contract of employment, and the terms of employment of the Executive or the relationship of the Executive with the Company or any subsidiary of the Company shall not be affected in any way by this Agreement except as specifically provided herein. The execution of this Agreement shall not be construed as conferring any legal rights upon the Executive for a continuation of employment or employment relationship with the Company or any subsidiary of the Company, nor (without limitation to the rights of the Executive under this Agreement) shall it interfere with the right of the Company or any subsidiary of the Company to discharge the Executive and to treat the Executive without regard to the effect which that treatment might have upon the Executive as a holder of the Restricted Shares.

i. Entire Agreement. This Agreement (including the Exhibits hereto) contains the entire understanding and agreement of the parties hereto concerning the subject matter hereof, and supersedes all earlier negotiations and understandings, written or oral, between the parties hereto with respect thereto.

j. Captions. The captions and headings of the sections and subsections of this Agreement are included for convenience only and are not to be considered in construing or interpreting this Agreement.

k. Counterparts. This Agreement may be executed in counterparts and by facsimile or electronic reproduction, each of which when signed by the Company or the Executive will be deemed an original and all of which together will be deemed the same agreement.

l. Assignment. This Agreement shall inure to the benefit of the successors of the Company and, subject to the restrictions on transfer herein set forth, be binding upon the Executive, his heirs, executors, administrators and successors. Neither party will be entitled to assign or transfer its rights or obligations under this Agreement, except with the prior written consent of the other.

m. Severability. This Agreement will be severable, and the invalidity or unenforceability of any term or provision hereof will not affect the validity or enforceability of this Agreement or of any other term or provision hereof. Furthermore, in lieu of any invalid or unenforceable term or provision, the parties hereto intend that there be added as a part of this Agreement a valid and enforceable provision as similar in terms to such invalid or unenforceable provision as may be possible.

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

The undersigned hereby accepts and agrees to all the terms and provisions of the foregoing Agreement.

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