Eastern Insurance (EIHI) 10-K 2012 FY Annual report

Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Eastern Insurance Holdings, Inc. (the “Company”) on Form 10-K for the period ended December 31, 2012, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Michael L. Boguski, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operation of the Company.

/S/    MICHAEL L. BOGUSKI

Michael L. Boguski

President and Chief Executive Officer

Dated: March 8, 2013