A sum-over-states perturbation theory is combined with density functional methodology (SOS-DFPT) and is applied to NMR shielding tenser calculations. Individual gauges for localized orbitals (IGLO) were used. Different types of approximations for the energy difference of the ground and "excited" states are compared. The calculations were carried out using a modified version of the deMon program. The results of NMR shielding tenser calculations using SOS-DFPT are in good agreement with those of the best post-Hartree-Fock approaches and also with experimental data. Results are presented for a number of organic and inorganic compounds (including transition metal complexes) and for a model dipeptide.