Exhibit 99.1

Endurance Reports Third Quarter 2013 Financial Results

PEMBROKE, Bermuda – November 4, 2013 – Endurance Specialty Holdings Ltd. (NYSE:ENH) today reported net income available to common shareholders of $75.2 million and $1.70 per diluted common share for the third quarter of 2013 versus net income of $31.9 million and $0.74 per diluted common share for the third quarter of 2012.

For the nine months ended September 30, 2013, Endurance reported net income available to common shareholders of $220.2 million and $5.04 per diluted common share versus net income of $170.6 million and $3.94 per diluted common share for the nine months ended September 30, 2012. Book value per diluted share was $54.33 at September 30, 2013, an increase of 4.6% from June 30, 2013 and up 2.7% from December 31, 2012.

Operating highlights for the quarter ended September 30, 2013 were as follows:

Operating highlights for the nine months ended September 30, 2013 were as follows:

John R. Charman, Chairman and Chief Executive Officer, commented, “Endurance had a good quarter, both financially and strategically. Financially, our strong operating results were driven by improved underwriting performance and positive investment returns. Strategically, we have made significant progress driving substantial improvements in our underwriting capabilities, streamlining our operations and enhancing our positioning in the global market. These strategies are accelerating. We continue to attract market leading talent and these new high quality growth initiatives combined with our more streamlined operations significantly improves our ability to transform Endurance into a world class underwriting organization with industry leading profitability.”

Insurance Segment

Operating highlights for Endurance’s Insurance segment for the quarter ended September 30, 2013 were as follows:

Operating highlights for Endurance’s Insurance segment for the nine months ended September 30, 2013 were as follows:

Net premiums written in the Insurance segment increased $3.1 million for the third quarter compared to the same period in 2012. Increases within the agriculture and casualty and other specialty lines of business were partially offset by declines in the professional and property lines of business. Within the agriculture line of business, net premiums written increased due to growth in spring crop policy counts and were partially offset by lower premiums from fall crops that were impacted by lower commodity prices compared to third quarter 2012. The increase in casualty and other specialty lines of business was predominantly driven by the addition of new underwriting teams in ocean and inland marine and within excess casualty. The decline in net premiums written in the professional line of business resulted from the termination of a program relationship in late 2012. The decline in property net premiums written reflects the nonrenewal of certain working layer property catastrophe contracts in order to improve the risk characteristics of the portfolio. For the nine months ended September 30, 2013, net premiums written declined $15.2 million as a decline in professional insurance was partially offset by growth in agriculture, property and casualty and other specialty lines of business.

The improvement in the Insurance segment combined ratio for the quarter ended September 30, 2013 compared to the same period in 2012 was primarily driven by lower net loss and acquisition expense ratios, partially offset by a higher general and administrative expense ratio. The biggest driver of the improvement in the net loss ratio resulted from a better crop year in the agriculture insurance line of business as 2012 was impacted by a severe drought. Also impacting the current quarter’s net loss ratio was improved accident year loss ratios in the property and casualty and other specialty lines of business that were partially offset by lower levels of prior period favorable reserve development. The general and administrative expense ratio was higher in the current quarter due to a greater level of corporate expenses related to severance costs, higher expenses associated with recently added underwriting teams and larger variable compensation expense accruals reflecting the Company’s higher current year profitability. For the nine months ended September 30, 2013, the combined ratio was 8.3 percentage points lower than the same period a year ago as lower net loss and acquisition expense ratios were partially offset by a higher general and administrative ratio.

Reinsurance Segment

Operating highlights for Endurance’s Reinsurance segment for the quarter ended September 30, 2013 were as follows:

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Operating highlights for Endurance’s Reinsurance segment for the nine months ended September 30, 2013 were as follows:

The $121.8 million decrease in net premiums written within the Reinsurance segment during the third quarter of 2013 compared to the third quarter of 2012 resulted primarily from declines in property, catastrophe and casualty reinsurance lines. The $67.2 million decline in property premiums in the current quarter compared to a year ago reflected a reduced participation on a few large contracts where pricing and terms were not adequate. The $23.9 million reduction in catastrophe premiums reflected the purchase of peak zone retrocessional coverage, which reduced net premiums written. Casualty premiums declined $24.1 million as the Company non-renewed business that no longer met profitability targets and a smaller level of premium adjustments were realized in the current quarter compared to a year ago. For the nine months ended September 30, 2013, net premiums written decreased $57.5 million due to declines within the property and catastrophe lines of business, partially offset by modest increases in the casualty and other specialty lines of business.

The combined ratio in the Reinsurance segment for the third quarter of 2013 increased modestly compared to the same period in 2012, predominantly due to a higher general and administrative expense ratio, partially offset by a lower net loss ratio. The net loss ratio in the third quarter of 2013 benefited from $41.9 million, or 16.0 percentage points, of favorable prior year loss reserve development, compared to $38.2 million, or 14.2 percentage points, for the same period a year ago. The favorable development in the current quarter was predominantly driven by short tail lines of business as losses have developed better than original estimates. The current quarter’s combined ratio also included 7.8 percentage points of catastrophe losses mainly related to hail storms in Germany, while the third quarter of 2012 included 5.3 percentage points of catastrophe losses relating to Hurricane Isaac and a number of small loss events. The higher general and administrative expenses were predominantly due to greater allocated corporate expenses related to severance costs from the reduction in senior executives previously announced and larger variable compensation expense accruals reflecting the Company’s higher current year profitability.

For the first nine months of 2013, the Reinsurance segment reported a combined ratio of 80.4% compared to 85.6% for the same period in 2012 principally due to a lower net loss ratio that included a greater level of favorable prior year loss reserve development, partially offset by a higher general and administrative expense ratio.

Investments

Endurance’s net investment income for the quarter and nine months ended September 30, 2013 was $38.1 million and $119.9 million, a decrease of $7.8 million and $14.9 million, respectively, compared to the same periods in 2012. The total return of Endurance’s investment portfolio was 1.32% and 0.68% for the quarter and nine months ended September 30, 2013, respectively, compared to 1.75% and 4.08% for the quarter and nine months ended September 30, 2012, respectively. Investment income generated from Endurance’s available for sale investments declined by $6.1 million and $19.6 million for the three and nine months ended September 30, 2013, respectively, compared to the same periods in 2012 due to lower reinvestment rates during 2013 and the short duration of Endurance’s fixed maturity portfolio. During the third quarter and nine months ended September 30, 2013, Endurance’s net investment income included gains of $13.2 million and $43.1 million, respectively, on its alternative investment funds and high yield loan funds, which are included in other investments, as compared to gains of $15.1 million and $38.1 million in the third quarter and first nine months of 2012, respectively. The ending book yield on Endurance’s fixed maturity investments at September 30, 2013 was 2.28%, down from 2.38% at September 30, 2012.

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At September 30, 2013, Endurance’s fixed maturity portfolio, which comprises 86.4% of Endurance’s investments, had an average credit quality of AA and a duration of 3.10 years. Endurance’s fixed maturity portfolio was in a net unrealized gain position of $59.7 million at September 30, 2013, a decrease of $82.0 million from December 31, 2012. Endurance recorded net realized investment losses, net of impairment losses recognized in earnings, of $6.8 million and gains of $8.4 million during the third quarter and first nine months of 2013 compared to net realized investment gains of $10.0 million and $29.5 million during the third quarter and first nine months of 2012.

Endurance ended the third quarter of 2013 with cash and invested assets of $6.4 billion, which represents a 3.2% decrease from December 31, 2012. Net operating cash outflow was $(16.6) million for the nine months ended September 30, 2013 versus $211.4 million inflow for the same period in 2012. The decline year over year was primarily due to the payment of claims related to prior years and a shift in settlement dates for agriculture insurance related receivables from the U.S. Federal Government.

Capitalization and Shareholders’ Equity

At September 30, 2013, Endurance’s shareholders’ equity was $2.84 billion or $54.33 per diluted common share versus $2.71 billion or $52.88 per diluted common share at December 31, 2012. For the quarter and nine months ended September 30, 2013, Endurance declared and paid common dividends of $0.32 and $0.96 per share, respectively. During the nine months ended September 30, 2013, the Company repurchased 318,252 common shares at an average cost of $45.83 per share. Total share repurchases amounted to $14.6 million for the nine months ended September 30, 2013. No common shares were repurchased during the third quarter of 2013.

Earnings Call

Endurance will host a conference call on November 5, 2013 at 8:30 a.m. Eastern time to discuss its financial results. The conference call can be accessed via telephone by dialing (888) 219-1420 or (913) 312-0420 (international) and entering pass code: 9454891. 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 November 19, 2013 by dialing (888) 203-1112 or (719) 457-0820 (international) and entering the pass code: 9454891.

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 third quarter of 2013 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, casualty and other specialty, professional lines and property lines of insurance and catastrophe, property, 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.

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, 2012.

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, 2012, 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.

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.

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 September 30, 2013 and 2012:

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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 nine months ended September 30, 2013 and 2012:

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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 three and nine months ended September 30, 2013 and 2012:

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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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