Exhibit 99.4

CONSENT TO BE NAMED AS TRUSTEE

The undersigned hereby consents: (i) to being named as a person who has agreed to serve as a trustee of Ellington Residential Mortgage REIT (the “Company”) upon the completion of the initial public offering of common shares described in the Company’s Registration Statement on Form S-11 (as amended or supplemented, the “Registration Statement”); and (ii) to the inclusion of his biographical information in the Registration Statement.

/s/ Thomas F. Robards

Thomas F. Robards

Dated: April 19, 2013