The virial theorem has been used to derive sum rules for dipole- and mixed-dipole-quadrupole nuclear electric shieldings and corresponding geometrical derivatives of dipole and quadrupole moments in a molecule. Test calculations have been carried out on a series of first- and second-row hydrides. The virial sum rules can be effective tools to prove the accuracy of theoretical nuclear shieldings and analytic geometrical derivatives. As the latter are related to ir intensities, the virial sum rules can give important indications on the reliability of theoretical predictions for this spectroscopical parameter.