Exhibit 99.1

Endurance Reports First Quarter 2014 Financial Results

PEMBROKE, Bermuda – May 5, 2014 – Endurance Specialty Holdings Ltd. (NYSE:ENH) today reported net income available to common shareholders of $96.3 million and $2.17 per diluted common share for the first quarter of 2014 versus net income of $92.1 million and $2.13 per diluted common share for the first quarter of 2013.

Operating highlights for the quarter ended March 31, 2014 were as follows:

John R. Charman, Chairman and Chief Executive Officer, commented, “During the first quarter we generated strong financial results as evidenced by our annualised operating return on equity of 15%. The transformation of Endurance began 12 months ago and as we promised, the much improved financial and operating performance is now emerging. This quarter our London Insurance underwriting platform is now fully staffed and we have realised significant, attractive, across-the-board premium growth from all our newly added US specialty underwriting teams. We successfully expanded our global specialty business whilst at the same time continuing the overall rebalancing and repositioning of our global reinsurance portfolio. From a strategic perspective we significantly increased our reinsurance purchasing activity across both our Insurance and Reinsurance portfolios to optimise the risk/ reward characteristics of our business.”

“Whilst we have planned for market conditions on both sides of our balance sheet to remain extremely challenging over the next couple of years, we have deliberately positioned Endurance to outperform in this environment. We remain dedicated to achieving superior returns for our valued shareholders.”

Insurance Segment

Operating highlights for Endurance’s Insurance segment for the quarter ended March 31, 2014 were as follows:

The Insurance segment’s first quarter gross premiums written were virtually unchanged from the first quarter a year ago as strong growth in professional lines and casualty and other specialty products was offset by declines in the agriculture line of business. Driven by newly added global teams of specialty underwriters, gross written premiums for professional

lines grew 85.0% while the casualty and other specialty lines of business expanded 32.6% compared to a year ago. Current quarter agriculture gross premiums written declined 6.5% from a year ago as the impact from reduced commodity prices was partially offset by a 6% increase in policy counts. Net premiums written in the first quarter declined 15.2% compared to a year ago as the Company purchased significantly greater reinsurance protection at very attractive terms, including a 10% whole account quota share across our entire Insurance segment’s portfolio and stop loss protection on our agriculture insurance business.

The improvement in the Insurance segment combined ratio for the quarter ended March 31, 2014 compared to the same period in 2013 was driven by lower net loss and acquisition expense ratios partially offset by a higher general and administrative expense ratio. The accident year net loss ratio in the first quarter of 2014 improved 7.5 percentage points compared to a year ago due to higher margin business underwritten by the global specialty underwriting teams added over the past 12 months. The acquisition expense ratio improved compared to a year ago due to higher ceding commissions on expanded reinsurance purchases. The general and administrative expense ratio was higher in the current quarter due to a smaller earned premium base and strategic investments being made within our global specialty insurance operations.

Reinsurance Segment

Operating highlights for Endurance’s Reinsurance segment for the quarter ended March 31, 2014 were as follows:

The decrease in gross premiums written within the Reinsurance segment during the first quarter of 2014 over the first quarter of 2013 resulted primarily from a continued rebalancing of the portfolio as selected non-renewals and price declines in catastrophe and casualty lines of business were partially offset by growth in property, professional lines and specialty lines of business. Catastrophe gross premiums written declined compared to a year ago reflecting lower pricing due to increased competition as well as our decision to reduce our participation on select contracts. The 34.3% reduction in the casualty line of business compared to the first quarter of 2013 was the result of the non-renewal of UK motor treaties and other non-renewals of business that did not meet our profitability targets. Attractive business generated from our newly hired U.S. and Zurich teams of underwriters drove growth in our professional lines, property and specialty lines of business. Net premiums written for the first quarter of 2014 declined 9.6% compared to the first quarter of 2013 as the Company ceded a greater portion of the catastrophe line of business and purchased aggregate excess of loss reinsurance covering the Company’s global catastrophe portfolio.

The combined ratio in the Reinsurance segment in the first quarter of 2014 improved compared to the same period in 2013 predominantly due to a lower net loss ratio partially offset by higher acquisition and general and administrative expense ratios. The current quarter’s net loss ratio improved compared to a year ago predominantly driven by a greater level of specialty business that generates higher margins. The net loss ratio in the first quarter of 2014 also benefited from 15.3 percentage points of favorable prior year loss reserve development across all lines of business, compared to 12.4 percentage points for the same period a year ago. The acquisition expense ratio was higher in the current quarter compared to a year ago as new business was generated from distribution sources with higher related acquisition costs. The general and administrative expense ratio increased due to higher allocated corporate expenses and a lower earned premium base compared to a year ago.

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Investments

Endurance’s net investment income for the quarter ended March 31, 2014 was $41.0 million, a decrease of $8.3 million compared to the same period in 2013. The total return of Endurance’s investment portfolio was 1.24% for the quarter ended March 31, 2014, compared to 0.60% for the quarter ended March 31, 2013. Investment income generated from Endurance’s available for sale investments increased by $0.8 million for the three months ended March 31, 2014 compared to the same period in 2013 due to modestly better returns during first quarter 2014 on Endurance’s fixed maturity portfolio. During the first quarter of 2014, Endurance’s net investment income included gains of $13.5 million on its alternative investment funds and high yield loan funds, which are included in other investments, as compared to gains of $23.1 million in the first quarter of 2013. The ending book yield on Endurance’s fixed maturity investments at March 31, 2014 was 2.04%, down from 2.36% at March 31, 2013.

At March 31, 2014, Endurance’s fixed maturity portfolio, which comprises 86.8% of Endurance’s investments, had an average credit quality of AA- and a duration of 2.94 years. Endurance’s fixed maturity portfolio was in a net unrealized gain position of $69.3 million at March 31, 2014, an increase of $23.4 million from December 31, 2013. Endurance recorded net realized gains, net of impairment losses recognized in earnings, of $4.8 million during the first quarter of 2014 compared to $5.4 million during the same period in 2013.

Endurance ended the first quarter of 2014 with cash and invested assets of $6.5 billion, which represents a 0.1% decrease from December 31, 2013. Net operating cash outflow was ($25.6) million for the quarter ended March 31, 2014 versus $23.5 million inflow for the same period in 2013. Net operating cash flows decreased compared to the same period in 2013 primarily due to reduced gross premium related cash inflows and higher ceded premium and general expenditure outflows, partially offset by lower gross loss payments.

Capitalization and Shareholders’ Equity

At March, 31, 2014, Endurance’s shareholders’ equity was $3.00 billion or $57.53 per diluted common share versus $2.89 billion or $55.18 per diluted common share at December 31, 2013. For the quarter ended March 31, 2014, Endurance declared and paid common dividends of $0.34 per share.

Earnings Call

Endurance will host a conference call on May 6, 2014 at 9:00 a.m. Eastern time to discuss its financial results. The conference call can be accessed via telephone by dialing (888) 539-3612 or (719) 325-2435 (international) and entering pass code: 2595909. Those who intend to participate in the conference call should register at least ten minutes in advance to ensure access to the call. A telephone replay of the conference call will be available through May 20, 2014 by dialing (888) 203-1112 or (719) 457-0820 (international) and entering the pass code: 2595909.

The public may access a live broadcast of the conference call at the “Investors” section of Endurance’s website, www.endurance.bm. Following the live broadcast, an archived version will continue to be available on Endurance’s website.

A copy of Endurance’s financial supplement for the first quarter of 2014 will be available on Endurance’s website at www.endurance.bm shortly after the release of earnings.

Operating income, operating return on average common equity, operating income per diluted common share, operating income allocated to common shareholders and the combined ratio excluding prior year net loss reserve development are non-GAAP measures. Reconciliations of these measures to the appropriate GAAP measures are included in the attached tables.

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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 agriculture, professional lines, property, and casualty and other specialty lines of insurance and catastrophe, property, casualty, professional lines and 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 Waterloo House, 100 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 “should,” “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, the effects of competitors’ pricing policies, greater frequency or severity of claims and loss activity, changes in market conditions in the agriculture insurance industry, termination of or changes in the terms of the U.S. multiple peril crop insurance program, a decreased demand for property and casualty insurance or reinsurance, changes in the availability, cost or quality of reinsurance or retrocessional coverage, our inability to renew business previously underwritten or acquired, our inability to maintain our applicable financial strength ratings, our inability to effectively integrate acquired operations, uncertainties in our reserving process, changes to our tax status, changes in insurance regulations, reduced acceptance of our existing or new products and services, a loss of business from and credit risk related to our broker counterparties, assessments for high risk or otherwise uninsured individuals, possible terrorism or the outbreak of war, a loss of key personnel, political conditions, changes in insurance regulation, changes in accounting policies, our investment performance, the valuation of our invested assets, a breach of our investment guidelines, the unavailability of capital in the future, developments in the world’s financial and capital markets and our access to such markets, government intervention in the insurance and reinsurance industry, illiquidity in the credit markets, changes in general economic conditions and other factors described in our Annual Report on Form 10-K for the year ended December 31, 2013.

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.

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ENDURANCE SPECIALTY HOLDINGS LTD.

CONSOLIDATED BALANCE SHEETS

(In thousands of United States dollars, except share and per share amounts)

Note: All financial information contained herein is unaudited, except the balance sheet data for the year ended December 31, 2013, which was derived from Endurance’s audited financial statements.

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ENDURANCE SPECIALTY HOLDINGS LTD.

CONSOLIDATED STATEMENTS OF INCOME

(In thousands of United States dollars, except share and per share amounts)

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ENDURANCE SPECIALTY HOLDINGS LTD.

RESULTS BY SEGMENT

(in thousands of United States dollars, except ratios)

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ENDURANCE SPECIALTY HOLDINGS LTD.

RESULTS BY SEGMENT

(in thousands of United States dollars, except ratios)

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ENDURANCE SPECIALTY HOLDINGS LTD.

CONSOLIDATED FINANCIAL RATIOS

As Reported

Effect of Prior Year Net Loss Reserve Development

Favorable / (Unfavorable)

Net of Prior Year Net Loss Reserve Development

The combined ratio is the sum of the loss, acquisition expense and general and administrative expense ratios. Endurance presents the combined ratio as a measure that is commonly recognized as a standard of performance by investors, analysts, rating agencies and other users of its financial information. The combined ratio, excluding prior year net loss reserve development, enables investors, analysts, rating agencies and other users of its financial information to more easily analyze Endurance’s results of underwriting activities in a manner similar to how management analyzes Endurance’s underlying business performance. The combined ratio, net of prior year net loss reserve development, should not be viewed as a substitute for the combined ratio.

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ENDURANCE SPECIALTY HOLDINGS LTD.

GROSS AND NET PREMIUMS WRITTEN BY SEGMENT

(in thousands of United States dollars)

The following tables show Endurance’s gross and net premiums written for the quarters ended March 31, 2014 and 2013:

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ENDURANCE SPECIALTY HOLDINGS LTD.

RECONCILIATIONS

(in thousands of United States dollars, except share, per share amounts and ratios)

The following is a reconciliation of Endurance’s net income, net income per diluted common share, net income allocated to common shareholders under the two-class method and annualized return on average common equity to operating income, operating income per diluted common share, operating income allocated to common shareholders under the two-class method and annualized operating return on average common equity (all non-GAAP measures) for the quarters ended March 31, 2014 and 2013:

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Operating income and operating income per diluted common share are internal performance measures used by Endurance in the management of its operations. Operating income allocated to common shareholders (excludes unvested restricted shares outstanding which are considered participating) per diluted common share represents operating income divided by weighted average dilutive common shares, which has been calculated in accordance with the two-class method under U.S. GAAP. Operating income represents after-tax operational results excluding, as applicable, after-tax net realized capital gains or losses and after-tax net foreign exchange gains or losses because the amount of these gains or losses is heavily influenced by, and fluctuates in part, according to the availability of market opportunities. Endurance believes these amounts are largely independent of its business and underwriting process and including them distorts the analysis of trends in its operations. In addition to presenting net income and net income per dilutive common share determined in accordance with the two-class method under GAAP, Endurance believes that showing operating income and operating income per dilutive common share enables investors, analysts, rating agencies and other users of its financial information to more easily analyze Endurance’s results of operations in a manner similar to how management analyzes Endurance’s underlying business performance. Operating income and operating income per dilutive common share should not be viewed as substitutes for GAAP net income and net income per dilutive common share, respectively.

Endurance presents return on equity as a measure that is commonly recognized as a standard of performance by investors, analysts, rating agencies and other users of its financial information.

Contact:

Investor Relations

Phone: +1 441 278 0988

Email: investorrelations@endurance.bm

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