We investigate 29Si nuclear magnetic resonance (NMR) chemical shifts, δiso, of silicon nitride. Our goal is to relate the local structure to the NMR signal and, thus, provide the means to extract more information from the experimental 29Si NMR spectra in this family of compounds. We apply structural modeling and the gauge-included projector augmented wave (GIPAW) method within density functional theory (DFT) calculations. Our models comprise known and hypothetical crystalline Si₃N₄, as well as amorphous Si₃N₄ structures. We find good agreement with available experimental 29Si NMR data for tetrahedral Si[4] and octahedral Si[6] in crystalline Si₃N₄, predict the chemical shift of a trigonal-bipyramidal Si[5] to be about -120 ppm, and quantify the impact of Si-N bond lengths on 29Si δiso. We show through computations that experimental 29Si NMR data indicates that silicon dicarbodiimide, Si(NCN)₂ exhibits bent Si-N-C units with angles of about 143° in its structure. A detailed investigation of amorphous silicon nitride shows that an observed peak asymmetry relates to the proximity of a fifth N neighbor in non-bonding distance between 2.5 and 2.8 Å to Si. We reveal the impact of both Si-N(H)-Si bond angle and Si-N bond length on 29Si δiso in hydrogenated silicon nitride structure, silicon diimide Si(NH)₂.