Robust regulatory signals in the cell often depend on interactions between short linear motifs (SLiMs) and globular proteins. Many of these interactions are poorly characterized because the binding proteins cannot be produced in the amounts needed for traditional methods. To address this problem, we developed a single-molecule off-rate (SMOR) assay based on microscopy of fluorescent ligand binding to immobilized protein partners. We used it to characterize substrate binding to the Anaphase-Promoting Complex/Cyclosome (APC/C), a ubiquitin ligase that triggers chromosome segregation. We find that SLiMs in APC/C substrates (the D box and KEN box) display distinct affinities and specificities for the substrate-binding subunits of the APC/C, and we show that multiple SLiMs in a substrate generate a high-affinity multivalent interaction. The remarkably adaptable substrate-binding mechanisms of the APC/C have the potential to govern the order of substrate destruction in mitosis.