Exhibit 10.3

FORM OF COMPANY LOCK-UP AGREEMENT

March 3, 2010

Max Capital Group Ltd.

Max House

2 Front Street

Hamilton, HM 11

Bermuda

Re: Max Capital Group Ltd. – Lock-Up Agreement

Ladies and Gentlemen:

1. In connection with the Agreement and Plan of Amalgamation (the “Plan of Amalgamation ”), dated as of March 3, 2010, by and among Harbor Point Limited, a Bermuda exempted company (the “Company”), Max Capital Group Ltd., a Bermuda exempted company (“Parent”), and Alterra Holdings Limited, a Bermuda exempted company and a wholly owned subsidiary of Parent (the “Amalgamation Sub”), the undersigned has agreed, as set forth below, to refrain from disposing of (a) the Class A voting common shares of the Company (“Company Common Shares”) and other securities of the Company and (b) the Parent voting common shares (the “Parent Common Shares”) and other securities of Parent acquired in the Amalgamation, in each case held by it subject to, and in accordance with, the terms set forth below. Capitalized terms used in this letter agreement (this “Agreement”) and not otherwise defined herein shall have the meanings assigned to them in the Plan of Amalgamation.

2. (a) The undersigned is the record and beneficial owner (as defined in Rule 13d-3 of the Exchange Act, which meaning will apply for all purposes of this Agreement whenever the term “beneficial” or “beneficially” is used), as of the date hereof, of the Company Common Shares, Company Stock Options and Company Restricted Shares and the Company Common Shares represented by the Warrant Percentage in the Company Warrants to the extent applicable set forth on Schedule I attached hereto, which as of March 3, 2010 (the “Reference Date”) constituted all of the Company Common Shares and other securities convertible into or exercisable for any Company Common Shares, whether vested or unvested, owned of record or beneficially by the undersigned.

(b) For the purpose of this Agreement, “Company Subject Shares” shall mean, collectively, the Company Common Shares, Company Stock Options and Company Restricted Shares and the Company Common Shares represented by the Warrant Percentage in the Company Warrants set forth on Schedule I attached hereto, together with (i) any Company Common Shares issued on the exercise of Company Stock Options and Company Warrants, (ii) any Company Restricted Shares that vest after the Reference Date and (iii) any Company Common Shares or other securities of the Company acquired following the Reference Date but prior to the Effective Time.

3. Effective as of the Effective Time, the Company Subject Shares owned by the undersigned will be converted into Parent Common Shares, Company Converted Restricted Shares, Company Converted Options and New Parent Warrants on the terms set forth in the Plan of Amalgamation (such Parent Common Shares, Company Converted Restricted Shares, Company Converted Options and New Parent Warrants together with (a) any Parent Common Shares issued on the exercise of such Company Converted Options and New Parent Warrants, (b) any Company Converted Restricted Shares that vest after the Effective Time and (c) any Company Subject Shares are collectively referred to as the “Subject Shares”). For the avoidance of doubt, Subject Shares shall not include Parent Common Shares or other securities of Parent acquired by the undersigned pursuant to any transaction other than the Amalgamation.

4. In consideration of the willingness of the Company, Parent and the Amalgamation Sub to enter into the Plan of Amalgamation, the benefits received by the undersigned in connection with the consummation of the Amalgamation, and of other good and valuable consideration the receipt and sufficiency of which is hereby acknowledged, the undersigned agrees that, during the period from the date of this Agreement until one hundred eighty (180) days following the Effective Time (the “Lock-Up Period”), subject to Section 5 below, the undersigned will not, and will not offer or agree to, directly or indirectly, (a) sell (including any short sale), transfer, tender, encumber, assign or otherwise dispose of or (b) enter into any contract, option, derivative, swap, hedging or other agreement or arrangement or understanding (including any profit or loss-sharing arrangement) with respect to or related to, any Subject Shares which the undersigned owns of record or beneficially, except (i) in a transaction required under applicable Law or (ii) with the prior written approval of at least a majority of the members of the board of directors of Parent. For the avoidance of doubt, the foregoing restrictions are expressly agreed to preclude the undersigned from engaging in any hedging or other transaction that is designed to or that reasonably could be expected to lead to or result in a sale or disposition of the Subject Shares (or the economic benefit thereof) even if such Subject Shares would be disposed of by someone other than the undersigned. Such prohibited hedging or other transactions would include without limitation any purchase, sale or grant of any right (including without limitation any put or call option) with respect to any of the Subject Shares or with respect to any security that includes, relates to, or derives any significant part of its value from such Subject Shares.

5. Notwithstanding the foregoing, the undersigned may (a) transfer Subject Shares to (i) any Affiliate of the undersigned or (ii) if the undersigned is an individual, to any Family Transferee; (provided, however, that in any such case, it shall be a condition to the transfer that the transferee execute an agreement stating that the transferee is receiving and holding any such Subject Shares subject to the provisions of this Agreement and there shall be no further transfer of such Subject Shares except in accordance with this Agreement), (b) with respect to any equity awards or warrants owned by the undersigned that would expire during the Lock-Up Period, surrender or otherwise dispose of such equity awards or warrants to the Company or Parent in connection with the exercise thereof and (c) sell, transfer, tender, assign, surrender or otherwise dispose of Subject Shares to Parent, the Company or to any other Person to satisfy the payment of withholding income or other applicable taxes resulting from the vesting or exercising of any equity awards of Parent or the Company owned of record or beneficially by the undersigned. In the case of a disposition under clause (c) above, the undersigned agrees to provide documentation and information to the Parent or the Company, as applicable, supporting

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the sale of a specified number of Company Common Shares or Parent Common Shares, as applicable, at least three (3) Business Days prior to any such disposition. The undersigned also agrees and consents to the entry of stop transfer instructions with Parent’s transfer agent and registrar against the transfer of the undersigned’s Subject Shares except in compliance with the foregoing restrictions. For the purposes of this Agreement, “Family Transferee” shall mean a (x) Shareholder’s spouse, immediate family members or lineal descendants or (y) any trust, the beneficiaries of which, or corporation, limited liability company or partnership, the shareholders, members or general or limited partners of which, include only persons described in clause (x). In addition, to the extent that the undersigned is an individual, the transfer restrictions set forth in this Agreement shall not apply following the undersigned’s death, termination of employment by Parent, the Company or any of their respective subsidiaries for “Disability,” termination of employment by Parent, the Company or any of their respective subsidiaries without “Cause,” termination of employment by the undersigned for “Good Reason,” termination of employment for “Retirement” or due to a “Change in Control” (each as defined in the applicable agreements between the undersigned and the Company).

6. Subject to paragraph 10 hereof, the undersigned hereby agrees that, until the Plan of Amalgamation is terminated in accordance with its terms, it shall, and shall use reasonable best efforts to cause its Representatives to, comply with the covenants set forth in Section 5.4(a) of the Plan of Amalgamation applicable to the Company as if such covenants were applicable to the undersigned.

7. The undersigned hereby acknowledges and agrees that it shall not be entitled to any Consideration or other payment in exchange for any equity or other interests in the Company owned of record or beneficially by the undersigned as of the Reference Date except as set forth on Schedule I attached hereto. The undersigned further agrees not to make any claim against Parent or any of its Affiliates (including the Amalgamated Company) following the Closing pursuant to Article II of the Plan of Amalgamation that is made in reliance on any fact or matter as of the Reference Date that is inconsistent with Schedule I attached hereto or its representations and warranties set forth in paragraph 2(a) hereof.

8. In the case of any undersigned who is not an individual, the undersigned hereby acknowledges and agrees that as of the Effective Time it shall not have any rights to appoint or nominate a director or observer or have any similar rights with respect to the board of directors of Parent or any of its Subsidiaries.

9. The undersigned hereby agrees to execute and deliver, on or prior to the date of the Company Shareholder Meeting, an instrument and other documents reasonably requested by Parent agreeing to and approving the termination of the Securityholders’ Agreement effective as of the Effective Time.

10. All agreements and understandings made herein shall be made solely in the undersigned’s capacity as a holder of Subject Shares and, to the extent the undersigned is a director or officer of the Company, not in the undersigned’s capacity as a director or officer of the Company. For the avoidance of doubt, Parent and the undersigned acknowledge and agree that (a) to the extent the undersigned is a director of the Company (or has a designee on the board of directors of the Company), the undersigned (or such designee) shall be free to act in his

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or her capacity as a director of the Company in accordance with his or her duties to the Company, (b) nothing herein shall prohibit or restrict any person described in clause (a) above from taking any action in facilitation of the exercise of his or her duties pursuant to the Plan of Amalgamation (including pursuant to Section 5.4 thereof) or otherwise, (c) to the extent the undersigned is an officer of the Company, nothing herein shall prohibit or restrict the undersigned from taking any action, or failing to take any action, in his or her capacity as an officer of the Company and in facilitation of the exercise of his or her duties to the Company as the undersigned determines in good faith is required to comply with the direction of the board of directors of the Company and (d) no action taken by any person described in clauses (a) through (c) above acting in the capacities described therein shall be deemed to be a breach or violation by the undersigned of this Agreement.

11. Except as expressly provided in this Agreement, the undersigned may not assign any rights or delegate any obligations under this Agreement without the prior written consent of Parent. Parent may not assign this Agreement without the prior written consent of the undersigned. Any such purported assignment or delegation made in violation of the foregoing shall be null and void (in addition to any other remedy to which the other party is entitled at law or in equity in connection with such violation).

12. The undersigned hereby permits the Company and Parent to publish and disclose in any proxy statement or prospectus (including any document or schedule filed with the SEC) the undersigned’s identity and ownership of Subject Shares and the nature of its commitments, arrangements and understandings pursuant to this Agreement.

13. This Agreement shall be governed in all respects, including as to validity, interpretation and effect, by the Laws of Bermuda, without giving effect to its principles or rules of conflict of Laws.

14. The parties agree that irreparable damage would occur in the event that any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached. It is accordingly agreed that the parties shall be entitled to an injunction or injunctions to prevent breaches of this Agreement and to enforce specifically the terms and provisions of this Agreement, this being in addition to any other remedy to which such party is entitled at law or in equity. Moreover, and in recognition of the foregoing, each of the parties hereby waives (a) any defense in any action for specific performance of this Agreement that a remedy at law would be adequate and (b) any requirement under any law for any party to post security as a prerequisite to obtaining equitable relief.

15. Each party irrevocably and unconditionally consents, agrees and submits to the jurisdiction of the Bermuda Supreme Court (and appropriate appellate courts therefrom) (the “Chosen Courts”), for the purposes of any litigation, action, suit or other proceeding arising out of this Agreement or any transaction contemplated hereby. Each party agrees to commence any litigation, action, suit or proceeding relating hereto only in the Bermuda Supreme Court, or if such litigation, action, suit or other proceeding may not be brought in such court for reasons of subject matter jurisdiction, in the other appellate courts therefrom or other courts of Bermuda. Each party irrevocably and unconditionally waives any objection to the laying of venue of any litigation, action, suit or proceeding arising out of this Agreement in the Chosen Courts, and

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hereby further irrevocably and unconditionally waives and agrees not to plead or claim in any such court that any such litigation, action, suit or proceeding brought in any such court has been brought in an inconvenient forum. The parties agree that a final judgment in any such litigation, action, suit or proceeding shall be conclusive and may be enforced in other jurisdictions by suit on the judgment or in any other manner provided by applicable Law.

16. The parties have participated jointly in negotiating and drafting this Agreement. In the event that an ambiguity or a question of intent or interpretation arises, this Agreement shall be construed as if drafted jointly by the parties, and no presumption or burden of proof shall arise favoring or disfavoring any party by virtue of the authorship of any provision of this Agreement. If any term or other provision of this Agreement is invalid, illegal or incapable of being enforced by any rule of law, or public policy, all other conditions and provisions of this Agreement shall nevertheless remain in full force and effect so long as the economic or legal substance of this Agreement is not affected in any manner adverse to any party. Upon such determination that any term or other provision is invalid, illegal or incapable of being enforced, the parties hereto shall negotiate in good faith to modify this Agreement so as to effect the original intent of the parties as closely as possible in a mutually acceptable manner in order that the terms of this Agreement remain as originally contemplated to the fullest extent possible.

17. This Agreement may not be amended except by an instrument in writing between the parties. Neither the failure nor any delay by any party hereto in exercising any right, power or privilege under this Agreement will operate as a waiver of such right, power or privilege, and no single or partial exercise of any such right, power or privilege will preclude any other or further exercise of such right, power or privilege or the exercise of any other right, power or privilege. In addition, (a) no claim or right arising out of this Agreement can be discharged by any party, in whole or in part, by a waiver or renunciation of the claim or right unless in writing signed by such party, (b) no waiver that may be given by any party will be applicable except in the specific instance for which it is given and (c) no notice to or demand on a party will be deemed to be a waiver of any obligation of such party and no notice from or demand by a party will be deemed to be a waiver of such party’s right to take further action without notice or demand as provided in this Agreement.

18. This Agreement, including the schedule attached hereto, contains the entire agreement between the parties concerning the subject matter hereof and supersedes and nullifies all prior agreements, understandings, discussions, negotiations and undertakings, whether written or oral, between the parties with respect to the subject matter hereof.

19. This Agreement may be executed in separate counterparts, each of which shall be considered one and the same agreement and shall become effective when each of the parties has delivered a signed counterpart to the other parties, it being understood that all parties need not sign the same counterpart. Delivery of an executed signature page of this Agreement by facsimile transmission or electronic “.pdf” shall be effective as delivery of a manually executed counterpart hereof.

20. This Agreement shall terminate automatically and without further action by any party on the earlier of (i) the date on which the Plan of Amalgamation is terminated in accordance with its terms and (ii) the expiration of the Lock-Up Period; provided that in the event the Closing occurs, paragraphs 2(a), 7, 8, 10, 13, 14, 15, 17 and this paragraph 19 shall survive indefinitely.

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The undersigned understands that the Company, Parent and the Amalgamation Sub are relying upon this Agreement in entering into the Plan of Amalgamation and in proceeding towards consummation of the Amalgamation. The undersigned further understands that this Agreement shall be binding upon the undersigned’s heirs, legal representatives, successors, and permitted assigns.

Schedule I

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