Exhibit 99.1

Endurance Provides Initial Loss Estimate from Superstorm Sandy

PEMBROKE, Bermuda—December 21, 2012—Endurance Specialty Holdings Ltd. (NYSE:ENH) today announced its initial loss estimate related to Superstorm Sandy, which made landfall in the Northeastern United States on October 29, 2012.

Endurance estimates that its losses related to Superstorm Sandy will be $160 million, pre-tax and net of reinsurance and reinstatement premium. Approximately $125 million of the estimated losses from Superstorm Sandy emanated from Endurance’s reinsurance segment, with the remainder of the estimated losses emanating from Endurance’s insurance segment.

Endurance’s loss estimate is preliminary and is largely derived from a combination of its proprietary catastrophe modeling, standard industry models, an in-depth review of in-force contracts and initial indications from clients and brokers. Endurance’s actual loss from Superstorm Sandy may ultimately differ materially from the initial estimated loss due to the size of the storm, the complexity of the assessment of damages and the limited number of reported claims received to date.

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, casualty, healthcare liability, agriculture, professional lines and surety and other specialty lines of insurance and property, catastrophe, casualty, aerospace and marine, and surety 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.

Safe Harbor for Forward-Looking Statements

Some of the statements in this press release may include forward-looking statements, which reflect our current views with respect to future events and financial performance. Such statements may include forward-looking statements both with respect to us in general and the insurance and reinsurance sectors specifically, both as to underwriting and investment matters. Statements which include the words “estimate,” “preliminary,” “expect,” “intend,” “plan,” “believe,” “project,” “anticipate,” “seek,” “will,” and similar statements of a future or forward-looking nature identify forward-looking statements in this press release for purposes of the U.S. federal securities laws or otherwise. We intend these forward-looking statements to be covered by the safe harbor provisions for forward-looking statements in the Private Securities Litigation Reform Act of 1995.

All forward-looking statements address matters that involve risks and uncertainties. Accordingly, there are or may be important factors that could cause actual results to differ from those indicated in the forward-looking statements. These factors include, but are not limited to, developments in the world’s financial and capital markets that could adversely affect the performance of Endurance’s investment portfolio or access to capital, changes in the composition of Endurance’s investment portfolio, competition, possible terrorism or the outbreak of war, the frequency or severity of unpredictable catastrophic events, changes in demand for insurance or reinsurance, rating agency actions, uncertainties in our reserving process, a change in our tax status, acceptance of our products, the availability of reinsurance or retrocessional coverage, retention of key personnel, political conditions, the impact of current regulatory investigations, changes in accounting policies, changes in general economic conditions and other factors described in our Annual Report on Form 10-K for the year ended December 31, 2011. In addition, the initial loss estimate relating to Superstorm Sandy is subject to adjustments, which may be material, as Endurance receives actual loss data from its clients.

Forward-looking statements speak only as of the date on which they are made, and we undertake no obligation publicly to update or revise any forward-looking statement, whether as a result of new information, future developments or otherwise.