Both four-component relativistic and nonrelativistic computations within the GIAO-DFT(PBE0) formalism have been carried out for 15N and 59Co NMR shielding constants and chemical shifts of a number of the nitrogen-coordinated complexes of cobalt. It was found that the total values of the calculated nitrogen chemical shifts of considered cobalt complexes span over a range of more than 580 ppm, varying from −452 to +136 ppm. At that, the relativistic corrections to nitrogen shielding constants and chemical shifts were demonstrated to be substantial, changing accordingly from ca. −19 to +74 ppm and from −68 to +25 ppm. Solvent effects on 15N shielding constants and chemical shifts were shown to have contributions no less important than the relativistic effects, namely from −35 to +63 ppm and from −74 to +23 ppm, respectively. Cobalt shielding constants and chemical shifts were found to vary in the ranges of, accordingly, −20,157 to −11,373 ppm and from +3781 to +13,811. The relativistic effects are of major importance in the cobalt shielding constants, resulting in about 4% for the shielding-type contributions, while solvent corrections to cobalt shielding constants appeared to be of less significance, providing corrections of about 1.4% to the gas phase values.