The influence of the optimized effective potential (OEP) and Coulomb-attenuation on shielding constants and chemical shifts is investigated for three disparate categories of molecule: main group, hydrogen bonded, and transition metal systems. Expanding the OEP in the orbital basis leads to physically sensible exchange-correlation potentials; OEP generalized gradient approximation results provide some indication of the accuracy of the expansion. OEP uncoupled magnetic parameters from representative hybrid and Coulomb-attenuated functionals can be a dramatic improvement over conventional results; both categories yield similar accuracy. Additional flexibility is introduced by expanding the OEP in an extensive even-tempered basis set, but this leads to the well-known problem of unphysical, oscillatory potentials. Smooth potentials are recovered through the use of a smoothing norm, but deficiencies in the procedure are highlighted for transition metal complexes. The study reiterates the importance of the OEP procedure in magnetic response calculations using orbital-dependent functionals, together with the need for careful attention to ensure physically sensible potentials. It also illustrates the utility of Coulomb-attenuated functionals for computing short-range molecular properties.