[Signature Page Follows]

Exhibit 2.1

June 4, 2009

IPC Holdings, Ltd.,

29 Richmond Road,

Pembroke HM 08,

Bermuda.

Ladies and Gentlemen:

Reference is made to the Agreement and Plan of Amalgamation dated as of March 1, 2009 and as amended March 5, 2009 (the “Agreement”), between IPC Holdings, Ltd., a Bermuda exempted company (“IPC”), IPC Limited, a Bermuda exempted company and a wholly-owned subsidiary of IPC, and Max Capital Group Ltd., a Bermuda exempted company (“Max”). Capitalized terms used, but not defined, herein shall have the meanings ascribed thereto in the Agreement.

Notwithstanding anything in the Agreement to the contrary, Max, IPC and IPC Limited agree that:

(i) IPC’s board of directors shall, as of the date hereof, declare a special dividend of $1.50 in cash per IPC Common Share outstanding (the “Special Dividend”) with a record date of June 15, 2009 and a payment date to occur one business day after the date on which the Effective Time occurs, the payment of which shall be conditional upon the Effective Time having occurred and subject to applicable laws, and the relevant board resolution declaring such dividend shall be substantially in the form attached as Annex A;

(ii) IPC’s board of directors shall, as of the date hereof, declare a special dividend of $1.00 in cash per IPC Common Share outstanding (the “Post-Closing Dividend”), with a record date of the twenty-first day after the date on which the Effective Time occurs (or the first business day thereafter, if such twenty-first day is not a business day) and a payment date one business day after the record date, the payment of which shall be conditional upon the Effective Time having occurred and subject to applicable laws, and the relevant board resolution declaring such dividend shall be substantially in the form attached as Annex A;

(iii) IPC shall not be required under Section 5.14 of the Agreement to coordinate with Max concerning the payment date for the Special Dividend or the Post-Closing Dividend and nothing in this letter shall be deemed to permit Max to declare or pay any special dividend;

(iv) IPC shall not be entitled, and IPC hereby waives its right under Section 7.1(g) of the Agreement, to terminate the Agreement if the total number of Dissenting Shares exceeds 15% of the issued and outstanding Max Common Shares;

(v) each of Max, IPC and IPC Limited hereby waives the requirement under Sections 5.1(b) and (c) of the Agreement that the IPC Shareholders Meeting and the Max Shareholders Meeting shall not occur prior to the third business day immediately following the last day on which the holders of Max Common Shares can require appraisal of their Max Common Shares pursuant to the Companies Act;

(vii) no representation, warranty, agreement or covenant of Max, IPC or IPC Limited contained in the Agreement shall be deemed to be inaccurate or breached as a result of the actions contemplated by the foregoing clauses (i) through (v).

This letter agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

Except to the extent expressly set forth herein, the terms, provisions and conditions of the Agreement shall remain unmodified and in full force and effect in all other respects.

[Signature Page Follows]

[Signature Page to the Waiver Agreement Letter]