Calculations of the g tensor of three copper(II) complexes [Cu(NH3)(4)](2-), [CuCl4](2-), and plastocyanin are presented. Two different sum-over-states-based approaches are considered, making use of the multistate CASPT2 method for excitation energies and PMCAS (perturbation modified CAS) wave functions for the computation of the angular momentum and spin-orbit coupling matrix elements. Test calculations on [Cu(NH3)(4)](2+) and [CuCl4](2-) point to the need of including in the MS-CASPT2 treatment the specific charge-transfer state with an electron excited out of the bonding counterpart of the ground-state SOMO. The computed g shifts for these two molecules present a considerable improvement with respect to the results obtained from our previous g tensor calculations based instead on CASSCF/CASPT2. This is shown to be related to an improved description of the covalency of the Cu-L bonds. For the calculations on plastocyanin, different models are used, taken from a recent (QM/MM) DFT study by Sinnecker and Neese. The effect of the surrounding protein is taken into account by surrounding the central cluster either with a dielectric continuum (epsilon = 4) or with a set of point charges. The second approach is found to be indispensable for an accurate description of environmental effects. With this approach, the calculated g values compare to within 30 ppt with the experimental data of plastocyanin.