Exhibit 99.1

 RMR MORTGAGE TRUST C/O BROADRIDGE FINANCIAL SOLUTIONS, INC. P.O. BOX 1342 BRENTWOOD, NY 11717 AUTHORIZE YOUR PROXY BY INTERNET - www.proxyvote.com Use the internet to transmit your voting instructions and for electronic delivery of information up until 11:59 p.m., Eastern time, on September 16, 2021. Have your proxy card in hand when you access the website and follow the instructions to obtain your records and to submit your voting instructions. AUTHORIZE YOUR PROXY BY TELEPHONE - 1-800-690-6903 Use any touch-tone telephone to transmit your voting instructions up until 11:59 p.m., Eastern time, on September 16, 2021. Have your proxy card in hand when you call and then follow the instructions. If the meeting is postponed or adjourned, the above times will be extended to 11:59 p.m., Eastern time, on the day before the reconvened meeting. AUTHORIZE YOUR PROXY BY MAIL Mark, sign and date your proxy card and return it in the postage-paid envelope we have provided or return it to RMR Mortgage Trust, c/o Broadridge, 51 Mercedes Way, Edgewood, NY 11717. VOTE BY VIRTUALLY ATTENDING THE MEETING During the Meeting - Go to www.virtualshareholdermeeting.com/RMRM2021SM You may attend the meeting via the Internet and vote during the meeting. Have your proxy card in hand when you access the website and follow the instructions provided on the website. ELECTRONIC DELIVERY OF FUTURE SHAREHOLDER COMMUNICATIONS If you would like to reduce the costs incurred by RMR Mortgage Trust in mailing proxy materials, you can consent to receiving all future proxy statements, proxy cards and annual reports electronically by email or over the internet. To sign up for electronic delivery, please follow the instructions above to vote using the internet and, when prompted, indicate that you agree to receive or access shareholder communications electronically in future years. TO VOTE, MARK BLOCKS BELOW IN BLUE OR BLACK INK AS FOLLOWS: D57756-TBD KEEP THIS PORTION FOR YOUR RECORDS THIS PROXY CARD IS VALID ONLY WHEN SIGNED AND DATED. DETACH AND RETURN THIS PORTION ONLY RMR MORTGAGE TRUST The Board of Trustees Recommends a Vote FOR Proposals 1 and 2. For Against Abstain ! !! ! !! THIS PROXY WHEN PROPERLY EXECUTED WILL BE VOTED AS DIRECTED OR, IF NO DIRECTION IS GIVEN, WILL BE VOTED FOR PROPOSALS 1 AND 2. TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, THE PROXIES, IN THEIR DISCRETION, ARE AUTHORIZED TO VOTE AND OTHERWISE REPRESENT THE UNDERSIGNED ON SUCH OTHER MATTERS AS MAY PROPERLY COME BEFORE THE MEETING OR AT ANY POSTPONEMENT OR ADJOURNMENT THEREOF. (NOTE: Please sign exactly as your name(s) appear(s) hereon. All holders must sign. When signing as attorney, executor, administrator or other fiduciary, please give full title as such. Joint owners should each sign personally. If a corporation, please sign in full corporate name by authorized officer, indicating title. If a partnership, please sign in partnership name by authorized person indicating title.) Signature [PLEASE SIGN WITHIN BOX]DateSignature (Joint Owners)Date

 RMR MORTGAGE TRUST SPECIAL MEETING OF SHAREHOLDERS Friday, September 17, 2021, 10:00 a.m., Eastern time Virtually via the Internet at www.virtualshareholdermeeting.com/RMRM2021SM Please see the Proxy Statement for attendance instructions. The Special Meeting of Shareholders of RMR Mortgage Trust will address the following items of business: Approval of the issuance of common shares of beneficial interest of RMR Mortgage Trust, in the merger of Tremont Mortgage Trust, a Maryland real estate investment trust, with and into RMR Mortgage Trust, with RMR Mortgage Trust as the surviving entity, pursuant to the Agreement and Plan of Merger, dated as of April 26, 2021, as it may be amended from time to time, by and between RMR Mortgage Trust and Tremont Mortgage Trust; and Approval of the adjournment of the special meeting of shareholders of RMR Mortgage Trust from time to time, if RMR Mortgage Trust deems it necessary or appropriate, to solicit additional proxies if there are not sufficient votes to approve such share issuance. THE BOARD OF TRUSTEES RECOMMENDS A VOTE FOR PROPOSALS 1 AND 2. D57757-TBD RMR MORTGAGE TRUST SPECIAL MEETING OF SHAREHOLDERS September 17, 2021, 10:00 a.m., Eastern time Proxy Important Notice Regarding the Availability of Proxy Materials: The proxy materials for the Special Meeting of Shareholders of RMR Mortgage Trust (the "Company"), including the Company's joint proxy statement/prospectus, are available on the internet. To view the proxy materials or authorize your proxy by internet, by telephone or by mail, please follow the instructions on the reverse side hereof. This proxy is solicited on behalf of the Board of Trustees of RMR Mortgage Trust. The undersigned shareholder of the Company hereby appoints Jennifer B. Clark, Matthew P. Jordan and Adam D. Portnoy, or any of them, as proxies for the undersigned, with full power of substitution in each of them, to attend this special meeting of shareholders of the Company to be held virtually via the Internet at www.virtualshareholdermeeting.com/RMRM2021SM, on Friday, September 17, 2021, at 10:00 a.m., Eastern time, and any postponement or adjournment thereof, to cast on behalf of the undersigned all the votes that the undersigned is entitled to cast at the meeting and otherwise to represent the undersigned at the meeting with all powers possessed by the undersigned if personally present at the meeting. The undersigned hereby acknowledges receipt of the joint proxy statement/prospectus, which includes the notice of this special meeting of shareholders, each of which is incorporated herein by reference, and revokes any proxy heretofore given with respect to the meeting. THE VOTES ENTITLED TO BE CAST BY THE UNDERSIGNED WILL BE CAST AS INSTRUCTED ON THE REVERSE SIDE HEREOF. IF THIS PROXY IS EXECUTED, BUT NO INSTRUCTION IS GIVEN, THE VOTES ENTITLED TO BE CAST BY THE UNDERSIGNED WILL BE CAST FOR PROPOSALS 1 AND 2. ADDITIONALLY, TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, THE VOTES ENTITLED TO BE CAST BY THE UNDERSIGNED WILL BE CAST BY THE PROXIES, IN THEIR DISCRETION, ON ANY OTHER MATTER THAT MAY PROPERLY COME BEFORE THE MEETING OR AT ANY POSTPONEMENT OR ADJOURNMENT THEREOF. See reverse for instructions on how to authorize a proxy.