We present the synthesis and magnetic characterization of a polycrystalline sample of the 6H-perovskite Ba3CeRu2O9, which consists of Ru dimers based on face-sharing RuO6 octahedra. Our low-temperature magnetic susceptibility, magnetization, and neutron powder diffraction results reveal a nonmagnetic singlet ground state for the dimers. Inelastic neutron scattering, infrared spectroscopy, and the magnetic susceptibility over a wide temperature range are best explained by a molecular orbital model with a zero-field splitting parameter D = 85 meV for the S-tot = 1 electronic ground-state multiplet. This large value is likely due to strong mixing between this ground-state multiplet and low-lying excited multiplets, arising from a sizable spin molecular orbital coupling combined with an axial distortion of the Ru2O9 units. Although the positive sign for the splitting ensures that Ba3CeRu2O9 is not a single molecule magnet, our work suggests that the search for these interesting materials should be extended beyond Ba3CeRu2O9 to other molecular magnets based on metal-metal bonding.