Temperature dependences of NMR chemical shifts of He-3 and Xe-129 in the liquid crystals K15 (5CB) and ZLI1167 orienting parallel and perpendicular to the external magnetic field, respectively, are measured. From the slopes of the He-3 shifts, their behaviour at the phase transition and from a comparison with corresponding data for Xe-129 shifts we conclude that the local shift anisotropy sigma(a) represents an important contribution to the 3He shifts. sigma(a) is responsible for the sign of the shift jump when going from the isotropic to the nematic phase, which is found positive in 5CB and negative in ZLI1167. By appropriate corrections for susceptibility and by scaling the He-3 van der Waals shift contributions from Xe-129 data the temperature dependence of sigma(a) for He-3 can be obtained. A theoretical model is introduced which explains the experimental results and shows that the sigma(a) values in the oriented phase are dominated by the isotropic susceptibility. In the isotropic phase however the susceptibility anisotropy is the determining factor.