Highly selective adhesion can be achieved between surfaces by patterning them with ripples. Materials with such surfaces are fabricated by successive molding of an elastomer, poly(dimethylsiloxane) (PDMS), against a master with a surface rippled by instability of a residually stressed surface thin film. Adhesion of interfaces between both complementary and non-complementary rippled surfaces was measured. Complementary surfaces showed significantly enhanced interfacial adhesion with increasing ripple amplitude. In contrast, interfaces with mismatched amplitudes had nearly negligible adhesion. Rate-dependence of adhesion in these surfaces was also studied. For complementary surfaces with low amplitudes we found a multiplicative coupling between the structure and rate enhancement of adhesion. A quantitative model developed for adhesion between complementary surfaces explains these observations.