EX-99.906CERT

Certification Pursuant to Section 906 of the Sarbanes-Oxley Act

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of Tortoise Energy Independence Fund, Inc. does hereby certify, to such officer’s knowledge, that the report on Form N-CSR of Tortoise Energy Independence Fund, Inc. for the period ended May 31, 2020 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable, and that the information contained in the Form N-CSR fairly presents, in all material respects, the financial condition and results of operations of Tortoise Energy Independence Fund, Inc. for the stated period.

/s/ P. Bradley Adams

P. Bradley Adams

Chief Executive Officer, Principal Financial
Officer and Treasurer

Tortoise Energy Independence Fund, Inc.

Dated: August 7, 2020

This certification is being furnished pursuant to Item 13(b) of Form N-CSR and Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed filed by Tortoise Energy Independence Fund, Inc. for purposes of Section 18 of the Securities Exchange Act of 1934.