In theory, both 501(c)(6) and (c)(3) organizations can offer certification; however, which type an organization is DOES MATTER, especially to the IRS. In short, most certifications are viewed by the IRS as primarily serving the profession rather than the public - thus a (c)(6) is appropriate and the certification revenue would be exempt from UBIT. However, a (c)(3) with substantial income from certification may be putting its status at risk. A (c)(3) with insubstantial income from certification does not put its status at risk; however, the certification income will likely be subject to UBIT.
That's an oversimplified explanation, so read the details in this article by lawyers at Venable LLC or this one by Pillsbury Winthrop Shaw Pittman lawyers (neither are new articles but the information is still current).