Using the multireference configuration interaction method due to Grimme and Waletzke, combined with the atomic mean-field approximations for the efficient calculation of spin-orbit matrix elements, the g-tensors in second-order perturbation theory have been calculated for the main group radicals CO+, CN, BO, BS, MgF, AlO, O-2, HCO, H2O+, NO2, CO2-, NF2, NO22-, O-3(-), ClO2, and H2CO+, and for the transition metal compounds ZnH, ZnF, and TiF3, using explicit sum-over-state expansions for up to 20 excited states. In most cases, a valence triple-zeta basis set with polarization functions has been employed. It is shown that the addition of diffuse functions to this basis set does not improve the g-tensor results, and in several instances leads to slower convergence of the sum-over-state expansion. The calculated g-tensors are in good agreement with experimental values, and with our previous multireference configuration interaction results available for 9 of the 19 radicals. Our results are shown to be equivalent to, or better than, values obtained by other theoretical methods. Examples of radicals for which g-tensor calculations presented problems in the past are AlO and TiF3. For AlO, we obtain Deltag(perpendicular to) = -1530 ppm (parts per million), compared with an experimental value of -1900 ppm in Ne matrix. Using the SVP (valence double-zeta plus polarization) basis set, Deltag(perpendicular to) of TiF3 is calculated to be -115.3 ppt (parts per thousand), compared with experimental values of -111.9 and -123.7 ppt. (C) 2003 American Institute of Physics.