We report $^{59}$Co, $^{93}$Nb, and $^{121}$Sb nuclear magnetic resonance (NMR) measurements combined with density functional theory (DFT) calculations on a series of half-Heusler semiconductors, including NbCoSn, ZrCoSb, TaFeSb and NbFeSb, to better understand their electronic properties and general composition-dependent trends. These materials are of interest as potentially high efficiency thermoelectric materials. Compared to the other materials, we find that ZrCoSb tends to have a relatively large amount of local disorder, apparently antisite defects. This contributes to a small excitation gap corresponding to an impurity band near the band edge. In NbCoSn and TaFeSb, Curie-Weiss-type behavior is revealed, which indicates a small density of interacting paramagnetic defects. Very large paramagnetic chemical shifts are observed associated with a Van Vleck mechanism due to closely spaced $d$ bands splitting between the conduction and valence bands. Meanwhile, DFT methods were generally successful in reproducing the chemical shift trend for these half-Heusler materials, and we identify an enhancement of the larger-magnitude shifts, which we connect to electron interaction effects. The general trend is connected to changes in $d$-electron hybridization across the series.