The computation of the electronic g tensor by two multireference methods is presented and applied to a selection of molecules including CN, BO, AIO, GaO, InO, ZnH, ZnF, O-2, H2O+, O-3(-), and H2CO+ (group A) as well as TiF3, CuCl42-, Cu(NH3)(4)(2+) and a series of d(1)-MOX4n- compounds, with M = V Cr, Mo, Tc, W, Re and X = F Cl, Br (group B). Two approaches are considered, namely, one in which spin-orbit coupling and the Zeeman effect are included using second-order perturbation theory and another one in which the Zeeman effect is added through first-order degenerate perturbation theory within the ground-state Kramers doublet. The two methods have been implemented into the MOLCAS quantum chemistry software package. The results obtained for the molecules in group A are in good agreement with experiment and with previously reported calculated g values. The results for the molecules in group B vary. While the g values for the d(1) systems are superior to previous theoretical results, those obtained for the d(9) systems are too large compared to the experimental values.