It has been a challenge to compute the poses and affinities for binding of peptides to proteins by molecular dynamics (MD) simulations. Such computations would be valuable for capturing the physics and the conformational freedom of the molecules, but they are currently too computationally expensive. Here we describe using MELD (Modeling Employing Limited Data)-accelerated MD for finding the binding poses and approximate relative binding free energies for flexible-peptide/protein interactions. MELD uses only weak information about the binding motif and not the detailed binding mode that is typically required by other free-energy-based methods. We apply this technique to study binding of P53-derived peptides to MDM2 and MDMX. We find that MELD finds correct poses, that the binding induces the peptide into the correct helical conformation, and that it is capable of roughly estimating relative binding affinities. This method may be useful in peptide drug discovery.