Exhibit 32.1

CERTIFICATIONS BY PRINCIPAL EXECUTIVE OFFICER AND

PRINCIPAL FINANCIAL OFFICER PURSUANT TO 18 U.S.C.

SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002*

I, Greg A. Tunney, certify, pursuant to Section 1350 of Chapter 63 of Title 18 of the United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge, the Annual Report of R.G. Barry Corporation on Form 10-K for the fiscal year ended June 30, 2012 (the “Annual Report”) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended, and that information contained in such Annual Report fairly presents, in all material respects, the consolidated financial condition and results of operations of R.G. Barry Corporation and its subsidiaries.

Date: September 12, 2012 |  | By: |  | /s/ Greg A. Tunney*
|  |  |  | Greg A. Tunney Title: President and Chief Executive Officer (Principal Executive Officer)

I, José G. Ibarra, certify, pursuant to Section 1350 of Chapter 63 of Title 18 of the United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge, the Annual Report of R.G. Barry Corporation on Form 10-K for the fiscal year ended June 30, 2012 (the “Annual Report”) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended, and that information contained in such Annual Report fairly presents, in all material respects, the consolidated financial condition and results of operations of R.G. Barry Corporation and its subsidiaries.

Date: September 12, 2012 |  | By: |  | /s/ José G. Ibarra*
|  |  |  | José G. Ibarra Title: Senior Vice President – Finance and Chief Financial Officer (Principal Financial Officer)

* | These certifications are being furnished as required by Rule 13a-14(b) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and Section 1350 of Chapter 63 of Title 18 of the United States Code, and shall not be deemed “filed” for purposes of Section 18 of the Exchange Act or otherwise subject to the liability of that Section. These certifications shall not be deemed to be incorporated by reference into any filing under the Securities Act of 1933, as amended, or the Exchange Act, except to the extent that R.G. Barry Corporation specifically incorporates these certifications by reference.