We have measured the surface energies of several viscoelastic polymers, using contact mechanics methods. The materials studied were diblock copolymers of poly(ethylene)-poly(ethylene-propylene) (PE-PEP) having different PE volume fractions and molecular weights. The materials exhibit differing viscoelastic relaxation functions in the bulk. Surface energies were determined from contact mechanics experiments in the loading mode, analyzed by incorporating the bulk viscoelastic effects into the Johnson-Kendall-Roberts theory of adhesive elastic contacts. The samples were made of spherical caps of the materials formed by first melting, and then cooling to room temperature. The measured values of the surface energies are close to the reported value for that : of the surface-active PEP block, based on prior contact angle measurements, indicating that reliable surface energy values can be extracted from contact mechanics experiments, suitably analyzed to account for viscoelastic behavior. We believe that this method may be generalizable to surface and interfacial energy studies of a wide range of viscoelastic polymers.