Exhibit 24.2

POWER OF ATTORNEY

The undersigned, John L. Harrington, hereby constitutes and appoints Matthew P. Jordan and G. Douglas Lanois, and each of them, with full power to act without the other, as his true and lawful attorney-in-fact and agent, with full power of substitution and resubstitution, for such person and in his name, place and stead, in any and all capacities, to sign any and all amendments and supplements to the registration statement on Form S-4 (File No. 333-256951) relating to the issuance of common shares of beneficial interest, $0.001 par value per share, of RMR Mortgage Trust, a Maryland statutory trust (“RMRM”), as contemplated by the Agreement and Plan of Merger, dated as of April 26, 2021, as it may be amended from time to time, or the Merger Agreement, by and between RMRM and Tremont Mortgage Trust, a Maryland real estate investment trust (“TRMT”), in the merger of TRMT with and into RMRM, with RMRM continuing as the surviving entity in the merger, including post-effective amendments, and any additional registration statement pursuant to Rule 462 under the Securities Act and other instruments necessary or appropriate in connection therewith, and to file the same, with all exhibits thereto, and other documents in connection therewith, with the United States Securities and Exchange Commission, and hereby grants to said attorneys-in-fact and agents, and each of them, full power and authority to do and perform each and every act and thing requisite and necessary or desirable to be done, and to take or cause to be taken any and all such further actions in connection with such registration statement as such attorneys-in-fact and agents, in each of their sole discretion, deems necessary or appropriate, as fully to all intents and purposes as he might or could do in person, hereby ratifying and confirming all that said attorney-in-fact and agent, or his substitute or substitutes, may lawfully do or cause to be done by virtue hereof.

Signature	Title	Date
/s/ John L. Harrington
John L. Harrington	Independent Trustee	June 17, 2021