EPR hyperfine coupling (hfc) constants were calculated for the isolated Cu(I)-NO system and various model complexes of this species with increasing number of oxygen-containing coligands. The influence of the basis sets, the computational level, and, especially, spin polarization effects on the isotropic and anisotropic life constants have been carefully explored. It turns out that it is rather difficult to obtain reliable Cu(I) hfc values for this system, in which a radical ligand is coordinated to a metal center with a formally closed-shell electron configuration. The spin density at the individual atomic centers is determined by two effects, the spin transfer from NO to unoccupied valence orbitals of Cu(I) and the spin polarization in formally doubly occupied orbitals of the system. A detailed analysis shows that both effects can yield large, but opposing contributions to the coupling constants. For copper, the anisotropic life constants are much more sensitive to the details of spin polarization than the isotropic one. For nitrogen, the situation is the opposite. It appears that it is difficult to describe the spin polarization quantitatively correctly by state-of-the-art density functional theory. For the type of systems under study, one has to conclude that experimentally obtained EPR parameters cannot be interpreted merely by the specific atomic contributions to the singly occupied molecular orbital. By considering model complexes with an increasing number of oxygen-containing coligands, we contribute to the interpretation of the EPR parameters that have been measured for the Cu(I)-NO species inside the ZSM-5 zeolite. Models with two or more oxygen neighbors rather well agree with the experiment. This is due to the additional charge transfer to the Cu(I) center caused by the coligands and the more realistic electrostatic potential around it.