Exhibit 99.1

Endurance Board of Directors Elects John R. Charman Chairman and Chief Executive Officer

PEMBROKE, Bermuda — May 28, 2013 — Endurance Specialty Holdings Ltd. (NYSE:ENH), a Bermuda-based specialty provider of property and casualty insurance and reinsurance, today announced that its Board of Directors has elected John R. Charman as the Company’s Chairman and Chief Executive Officer, effective immediately. David Cash has stepped down as the Company’s Chief Executive Officer and as a member of the Board. William H. Bolinder, the current Chairman of the Board, has become the Company’s Lead Director.

Prior to his joining Endurance, Mr. Charman, together with members of his family, became one of its largest shareholders with the purchase of $30 million of the Company’s ordinary shares and indicated their intent to reinvest the dividends received on their investment.

Mr. Charman, 60, has four decades of global experience in the insurance industry, has been in a senior underwriting position since 1975 and has been in a CEO role since 1981. Most recently, he founded and served for 11 years as the Chief Executive Officer and President of Axis Capital Holdings Limited. Prior to that, Mr. Charman was the Chief Executive Officer of Tarquin plc, the parent company of the Charman Underwriting Agencies at Lloyd’s, which was sold to Ace Limited in 1998. Mr. Charman was a Deputy Chairman of the Council of Lloyd’s and a member of the Lloyd’s Core Management Group and Lloyd’s Market Board between 1995 and 1997 during the financial crisis at Lloyds.

William H. Bolinder, Lead Director, said: “John Charman brings to Endurance outstanding leadership qualities, global insurance experience and the demonstrated ability to attain strong and consistent operating performance. John has a blue chip track record of delivering bottom-line results, improving underwriting ratios, managing risk and allocating capital efficiently. We believe the opportunity to benefit from his expertise is extraordinary and look forward to him helping Endurance build on its success to date while enhancing our focus on shareholder value creation. His investment of personal capital speaks volumes about his confidence in and commitment to our future opportunities.”

Mr. Bolinder continued. “On behalf of the entire Board, I would like to thank David for his 11 years of service to Endurance, the last three as Chief Executive Officer. The Board is grateful to David for his valuable leadership and dedication to Endurance and the work he has done to position the Company well for the future. We wish him all the best with the next stage of his career.”

Mr. Charman said: “Endurance is a great company with great people and significant future potential. The Company’s high standing is a testament to the efforts and hard work of its employees. In support of my strong belief and commitment to Endurance’s future and to fully align myself with the Company’s shareholders, I am investing a significant amount of my own capital in Endurance as well as foregoing any conventional compensation over the next five years in exchange for a single grant of restricted shares and options. I am really looking forward to working with and closely supporting Endurance’s senior management team, employees and directors as well as our valued customers and brokers. My goal is to fully realize the Company’s potential as a leading global specialty insurance and reinsurance company.”

As an inducement to his employment with Endurance, Mr. Charman will receive a stock option to purchase 800,000 ordinary shares at an exercise price equal to the opening price of Endurance’s ordinary shares on May 28, 2013, and a grant of 708,890 restricted shares. The awards will vest over the next four years, subject to Mr. Charman’s continued employment, or in the event of certain terminations of employment and other events. Mr. Charman will receive a minimal base salary and no incentive compensation over the next five years. This announcement is made pursuant to the Corporate Governance Standards of NYSE Rule 303A.08. For the further details regarding Mr. Charman’s employment and compensation, please see the Company’s Current Report on Form 8-K to be filed on or before June 3, 2013 with the U.S. Securities and Exchange Commission.

Mr. Charman’s appointment is subject to the approval of the Bermuda Department of Immigration.

About Endurance Specialty Holdings

Endurance Specialty Holdings Ltd. is a global specialty provider of property and casualty insurance and reinsurance. Through its operating subsidiaries, Endurance writes property, agriculture, professional lines, and casualty and other specialty lines of insurance and property, catastrophe, casualty, and other specialty lines of reinsurance. We maintain excellent financial strength as evidenced by the ratings of A (Excellent) from A.M. Best (XV size category) and A (Strong) from Standard and Poor’s on our principal operating subsidiaries. Endurance’s headquarters are located at Wellesley House, 90 Pitts Bay Road, Pembroke HM 08, Bermuda and its mailing address is Endurance Specialty Holdings Ltd., Suite No. 784, No. 48 Par-la-Ville Road, Hamilton HM 11, Bermuda. For more information about Endurance, please visit www.endurance.bm.

Contact

Investor Relations

Phone: (441) 278-0988

Email: investorrelations@endurance.bm

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