Exhibit (b)

Certification

I, Jonathan Gans, Chief Executive Officer and President of Ironwood Institutional Multi-Strategy Fund LLC (the “Fund”), certify that:

  1.   The Form N-CSR of the Fund (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Certification

I, Martha Boero, Treasurer of Ironwood Institutional Multi-Strategy Fund LLC (the “Fund”), certify that:

  1.   The Form N-CSR of the Fund (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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