Seneca Global Fund, L.P. 10-Q

EXHIBIT 32.01

Certification Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the quarterly report of Seneca Global Fund, L.P. (“Fund”), on Form 10-Q for the quarter ended March 31, 2015, as filed with the U.S. Securities and Exchange Commission on the date hereof (“Report”), I, Kenneth E. Steben, President and Chief Executive Officer of Steben & Company, Inc., the General Partner of the Fund, certify, pursuant to §906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. §1350), that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the U.S. 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 operations of the Fund.

Date: May 15, 2015