The computational identification of peptides that can bind the major histocompatibility complex (MHC) with high affinity is an essential step in developing personal immunotherapies and vaccines. We introduce PUFFIN, a deep residual network-based computational approach that quantifies uncertainty in peptide-MHC affinity prediction that arises from observational noise and the lack of relevant training examples. With PUFFIN’s uncertainty metrics, we define binding likelihood, the probability a peptide binds to a given MHC allele at a specified affinity threshold. Compared to affinity point estimates, we find that binding likelihood correlates better with the observed affinity and reduces false positives in high-affinity peptide design. When applied to examine an existing peptide vaccine, PUFFIN identifies an alternative vaccine formulation with higher binding likelihood. PUFFIN is freely available for download at http://github.com/gifford-lab/PUFFIN.