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 StemCells, Inc. (the “Company”) quarterly report on Form 10-Q for the period ending June 30, 2013 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Martin McGlynn, 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 the best of my knowledge:

(1) 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 Company.

A signed original of this written statement required by Section 906 has been provided to StemCells, Inc. and will be retained by StemCells, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.

Date August 7, 2013

/s/ Martin McGlynn

Martin McGlynn

President and Chief Executive Officer