The northern clingfish (Gobiesox maeandricus) has a suction-based adhesive disc that can stick to incredibly rough surfaces, a challenge for stiff commercial suction cups. Both clingfish discs and bioinspired suction cups have stiff cores but flexible edges that can deform to overcome surface irregularities. Compliant surfaces are common in nature and technical settings, but performance data for fish and commercial cups are gathered from stiff surfaces. We quantified the interaction between substrate compliance, surface roughness and suction performance for the northern clingfish, commercial suction cups and three biomimetic suction cups with disc rims of varying compliance. We found that all cups stick better on stiffer substrates and worse on more compliant ones, as indicated by peak stress values. On compliant substrates, surface roughness had little effect on adhesion, even for commercial cups that normally fail on hard, rough surfaces. We propose that suction performance on compliant substrates can be explained in part by effective elastic modulus, the combined elastic modulus from a cup–substrate interaction. Of all the tested cups, the biomimetic cups performed the best on compliant surfaces, highlighting their potential to be used in medical and marine geotechnical fields. Lastly, we discuss the overmolding technique used to generate the bioinspired cups and how it is an important tool for studying biology.