The monopositive scandium and titanium carbides, ScC+ and TiC+, have been studied by multireference methods coupled with quantitative basis sets. We have constructed potential energy curves for the ground and twelve low-lying excited states for both species, focusing on dissociation energies and bonding mechanisms. We have found that the ground states of ScC+ and TiC+ are of (3)Pi and (2)Sigma (+) symmetries, with binding energies (D-0) of 68.8 (71.5) and 85.2 (86.7) kcal/mol at the MRCI (MRCI+Davidson correction) level of theory. These values are compared favorably with the corresponding experimental findings, D-0(ScC+) = 77.0 +/- 1.4 and D-0(TiC+) = 93.4 +/- 5.5 kcal/mol.