The application of the frozen core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed, and an implementation is presented. A complete formulation of the shielding calculation within the frozen core approximation is given, both in general terms and for the special case of density functional theory (DFT) and "gauge including atomic orbitals" (GIAO's). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen core approximation is a useful tool for shielding calculations -- if the valence space is increased to contain at least the ns, np, (n-1)p, (n-1)d (fourth period and higher) shells where n is the number of the given period in the periodic table of elements. The new method is applied to 77Se shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts whereas calculated absolute shieldings are generally too small by about 300 to 400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitely incorporated into the experimental absolute shielding scale.