The precise atomic structure of a metal contact significantly affects the performance of nanoscale electronic devices. We use an accurate, DFT-based non-equilibrium Green’s function method to evaluate various metal contacts with graphene or graphene nanoribbons. For surface metal contacts not chemically bound to graphene, Ti contacts have lower resistance than those of Au, Ca, Ir, Pt, and Sr. However, as an edge contact, Ti has larger resistance than Au. Bridging O atoms at Ti and Au edge contacts lowers the transmission by over 30%.