Exhibit 10.2

EXECUTION VERSION

FOURTH SUPPLEMENTAL INDENTURE

BY AND BETWEEN

ENDURANCE SPECIALTY HOLDINGS LTD.,

AS ISSUER

AND

THE BANK OF NEW YORK MELLON,

AS TRUSTEE

DATED AS OF JULY 31, 2015

FOURTH SUPPLEMENTAL INDENTURE

FOURTH SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of July 31, 2015, between ENDURANCE SPECIALTY HOLDINGS LTD., a Bermuda exempted company (the “New Issuer”), and THE BANK OF NEW YORK MELLON (as successor to The Bank of New York), as trustee under the Indenture referred to below (the “Trustee”).

RECITALS

WHEREAS, Montpelier Re Holdings Ltd., a Bermuda exempted company (“Montpelier”), has heretofore executed and delivered to the Trustee an indenture dated as of July 15, 2003, between Montpelier, as issuer, and the Trustee, as supplemented by the First Supplemental Indenture thereto, dated as of July 30, 2003 (the “First Supplemental Indenture”), as further supplemented by the Second Supplemental Indenture thereto, dated as of October 5, 2012 (the “Second Supplemental Indenture”), and the Third Supplemental Indenture thereto, dated as of July 31, 2015, between Millhill Holdings Ltd. (“Merger Sub”), as successor to Montpelier, and the Trustee (the “Third Supplemental Indenture”) (as heretofore amended, supplemented or otherwise modified by the First Supplemental Indenture, the Second Supplemental Indenture and the Third Supplemental Indenture, the “Indenture”) (capitalized terms used herein but not otherwise defined shall have the meanings ascribed to them in the Indenture);

WHEREAS, pursuant to the Agreement and Plan of Merger, dated March 31, 2015, among the New Issuer, Merger Sub and Montpelier, Montpelier will merge with and into Merger Sub, with Merger Sub surviving the merger as a direct, wholly-owned subsidiary of the New Issuer;

WHEREAS, pursuant to the Deed of Merger, dated July 31, 2015, between the New Issuer and Merger Sub, Merger Sub merged with and into New Issuer, with New Issuer being the surviving company of such merger.

WHEREAS, Section 11.1 of the Indenture provides that if Merger Sub merges into another Person, the Person into which Merger Sub is merged (1) shall be a Corporation or limited liability company organized and existing under the laws of the United States of America, any state thereof or the District of Columbia, Bermuda, or any other country (including under the laws of any state, province or other political subdivision thereof) which is on the date of the Indenture (or, with respect to the Notes issued pursuant to the Second Supplemental Indenture, the date of the Second Supplemental Indenture) a member of the Organization for Economic Cooperation and Development and (2) shall expressly assume, by an indenture (or indentures, if at such time there is more than one Trustee) supplemental thereto, executed by the successor Person and delivered to the Trustee, the due and punctual payment of the principal of, any premium and interest on and any Additional Amounts with respect to all the Securities and the performance of every obligation in the Indenture and the Outstanding Securities on the part of Merger Sub to be performed or observed and shall provide for conversion or exchange rights in accordance with the provisions of the Securities of any series that are convertible or exchangeable into Common Stock or other securities;

2

WHEREAS, the New Issuer is a Bermuda exempted company;

WHEREAS, Section 10.1 of the Indenture provides that without the consent of any Holders, Merger Sub, when authorized by a Board Resolution, and the Trustee may enter into a supplemental indenture to evidence the succession of another Person to Merger Sub, or successive successions, and the assumption by the successor Person of the covenants, agreements and obligations of Merger Sub under the Indenture and the Securities, in each case in compliance with the Indenture; and

WHEREAS, all acts and requirements necessary to authorize the execution and delivery of this Supplemental Indenture have been done or performed.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the New Issuer and the Trustee mutually covenant and agree as follows:

ARTICLE I

Successor Issuer

Section 1.1 Agreement to Assume Obligations. The New Issuer hereby agrees to unconditionally assume the due and punctual payment of the principal of, any premium and interest on and any Additional Amounts with respect to all the Securities and the performance of every obligation in the Indenture and the Outstanding Securities on the part of Merger Sub to be performed or observed.

Section 1.2 Notices. All notices or other communications to the New Issuer shall be given as provided in Section 13.5 of the Indenture, as amended by the Third Supplemental Indenture, at the address provided therein for the Company.

Section 1.3 Release of Obligations of Merger Sub. Merger Sub is hereby automatically released and discharged from all obligations under the Indenture and the Securities, without any further action on the part of Merger Sub or the Trustee.

ARTICLE II

Miscellaneous Provisions

Section 2.1 Ratification and Incorporation of Indenture. As supplemented hereby, the Base Indenture is in all respects ratified and confirmed, and the Base Indenture as supplemented by this Supplemental Indenture shall be read, taken and construed as one and the same instrument. However, to the extent any provision of the Base Indenture conflicts with the express provisions of this Supplemental Indenture, the provisions of this Supplemental Indenture will govern and be controlling.

3

Section 2.2 Counterparts. This Supplemental Indenture may be executed in several counterparts, each of which shall be an original and all of which shall constitute but one and the same instrument.

Section 2.3 Governing Law. This Supplemental Indenture and the rights and obligations of each of the Holders, the New Issuer and the Trustee shall be construed and enforced in accordance with and governed by the laws of the State of New York without reference to its conflict of laws provisions (other than Sections 5-1401 and 5-1402 of the General Obligations Law).

Section 2.4 Headings. The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

Section 2.5 Trustee. The Trustee makes no representations as to the validity or sufficiency of this Supplemental Indenture. The recitals and statements herein are deemed to be those of the New Issuer and not of the Trustee.

Section 2.6 Separability: In case any provision of this Supplemental Indenture or of the Securities shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

Section 2.7 Submission to Jurisdiction: ANY JUDICIAL PROCEEDINGS INSTITUTED IN RELATION TO ANY MATTER ARISING UNDER THIS SUPPLEMENTAL INDENTURE, THE SECURITIES APPERTAINING THERETO MAY BE BROUGHT IN ANY UNITED STATES FEDERAL OR NEW YORK STATE COURT SITTING IN THE BOROUGH OF MANHATTAN, THE CITY OF NEW YORK, NEW YORK TO THE EXTENT THAT SUCH COURT HAS SUBJECT MATTER JURISDICTION OVER THE CONTROVERSY, AND, BY EXECUTION AND DELIVERY OF THIS SUPPLEMENTAL INDENTURE, THE NEW ISSUER HEREBY IRREVOCABLY ACCEPTS, GENERALLY AND UNCONDITIONALLY, THE JURISDICTION OF THE AFORESAID COURTS, ACKNOWLEDGES THEIR COMPETENCE AND IRREVOCABLY AGREES TO BE BOUND BY ANY JUDGMENT RENDERED IN SUCH PROCEEDING. THE NEW ISSUER ALSO IRREVOCABLY AND UNCONDITIONALLY WAIVES FOR THE BENEFIT OF THE TRUSTEE AND THE HOLDERS OF THE SECURITIES ANY IMMUNITY FROM JURISDICTION AND ANY IMMUNITY FROM LEGAL PROCESS (WHETHER THROUGH SERVICE OR NOTICE, ATTACHMENT PRIOR TO JUDGMENT, ATTACHMENT IN THE AID OF EXECUTION, EXECUTION OR OTHERWISE) IN RESPECT OF THIS SUPPLEMENTAL INDENTURE. NOTHING HEREIN SHALL AFFECT THE RIGHT TO SERVE PROCESS IN ANY OTHER MANNER PERMITTED BY ANY LAW OR LIMIT THE RIGHT OF THE TRUSTEE OR ANY HOLDER TO INSTITUTE PROCEEDINGS AGAINST THE NEW ISSUER IN THE COURTS OF ANY OTHER JURISDICTION OR JURISDICTIONS.

[SIGNATURE PAGE FOLLOWS]

4

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the date first above written.

[Signature Page to Fourth Supplemental Indenture]

Acknowledged by:

MILLHILL HOLDINGS LTD.

[Signature Page to Fourth Supplemental Indenture]