A cleaning composition and process for cleaning an in-process microelectronic device substrate, e.g., by post-chemical mechanical polishing (CMP) cleaning, to remove residue from a surface thereof, wherein the cleaning composition may be especially effective for cleaning a substrate surface that includes exposed metal such as cobalt, copper, or both, along with dielectric or low k dielectric material, and wherein the cleaning composition includes corrosion inhibitor to inhibit corrosion of the exposed metal.