Fully relativistic four-component Dirac-Fock Coulomb calculations in conjunction with a second-order perturbational estimate for the correlation energy have been performed in benchmark calculations on geometric and electronic structures as well as the binding energy of the cationic platinum carbene complex PtCH2+. The relativistic stabilization of this species amounts to as much as 50 kcal/mol and the combination of relativistic and correlation effects shorten the Pt-C bond length by nearly 1 bohr, changing the bond order from one to two. The relative importance of spin-free and spin-dependent relativistic effects on the geometry, the electronic structure, and the binding energy is evaluated by comparison to the Douglas-Kroll method. Relativistic effective core potentials are shown to describe the spin-free effects reliably. The best theoretical estimate for the bond dissociation energy underestimates the experimental value by 13% due to truncation errors in the one- and n-particle space treatments. The mixed Hartree-Fock/density-functional method Becke3-Lee-Yang-Parr performs surprisingly well with respect to the structure and binding energy of the target molecule.