Modern density functional methods have been used to study spin-density distribution, g tensors, as well as Cu and ligand hyperfine tensors for azurin models, for two more blue copper proteins plastocyanin and stellacyanin, and for small model complexes. The aim was to establish a consistent computational protocol that provides a realistic description of the EPR parameters as probes of the spin-density distribution between metal and coordinated ligands in copper proteins. In agreement with earlier conclusions for plastocyanin, hybrid functionals with appreciable exact-exchange admixtures, roughly around 50%, provide the best overall agreement with all parameters. Then the bulk of the spin density is almost equally shared by the copper atom and the sulfur atom of the equatorial cysteine ligand, and the best values are obtained for copper, histidine nitrogen, and cysteine beta-proton hyperfine couplings, as well as for g(parallel to). Spin-orbit effects on the EPR parameters may be appreciable and have to be treated carefully to obtain agreement with experiment. Most notably, spin-orbit effects on the Cu-65 hyperfine coupling tensors in blue copper sites are unusually large compared to more regularly coordinated Cu-II complexes with similar spin density on copper. In addition to the often emphasized high covalency of the Cu-S(Cys) bond, the characteristically small A(parallel to) component of blue copper proteins is shown to derive to a large part from a near-cancellation between negative first-order (Fermi contact and dipolar) and unusually large positive second-order (spin-orbital) contributions. The large spin-orbit effects relate to the distorted tetrahedral structures. Square planar dithiolene complexes with similar spin density on copper exhibit much more negative A(parallel to) values, as the cancellation between nonrelativistic and spin-orbit contributions is less complete. Calculations on a selenocysteine-substituted variant of azurin have provided further insight into the relations between bonding and EPR parameters.