We present the gauge invariant atomic orbital (GIAO) calculation of nuclear magnetic shieldings for solvated molecules described within the polarizable continuum model (PCM). The performance of the PCM-GIAO approach is tested in a benchmark calculation of isotropic C-13, N-15, and O-17 shielding constants for CH3CN and CH3NO2 in vacuo and in water, both at the Hartree-Fock and density functional levels of theory. Various aspects of the calculation of solvent effects on these properties, such as the dependence on the basis set, the electron correlation, and the size of the molecular cavity embedding the solute, are taken into account and discussed. An interpretation of the gas-to-solution shielding variations in terms of a combined action of the solvent reaction field and the shielding polarizabilities is also given.