Traditionally, computing the binding affinities of proteins to even relatively small and rigid ligands by free-energy methods has been challenging due to large computational costs and significant errors. Here, we apply a new molecular simulation acceleration method called MELD (Modeling by Employing Limited Data) to study the binding of stapled α-helical peptides to the MDM2 and MDMX proteins. We employ free-energy-based molecular dynamics simulations (MELD-MD) to identify binding poses and calculate binding affinities. Even though stapled peptides are larger and more complex than most protein ligands, the MELD-MD simulations can identify relevant binding poses and compute relative binding affinities. MELD-MD appears to be a promising method for computing the binding properties of peptide ligands with proteins.