We apply our recently developed methodology for first-principles computations of paramagnetic NMR shieldings and explore the shieldings in a selected set of radicals that form core units in molecular magnets. The influence on these parameters of hydrogen bonding, that corresponds to the crystal environment, is the prime objective of the study. Nitronylnitroxide radicals with the hydroxyphenyl group in the ortho, meta, and para positions, as well as p-methoxyphenyl derivatives, are chosen for this purpose. The strong (NOHO)-H-... hydrogen bonding in the real crystal structure has been simulated by adding water molecules in the twelve molecular complexes investigated. Comparison of calculated and experimental data is made by taking the special features of the solid state and solution environments into account. The observed change in the shielding constant due to hydrogen bonding is explained by the spin delocalization picture; the dominating contribution is the temperature-dependent contact shielding containing the isotropic hyperfine coupling constant.