Self-consistent quasiparticle GW (sc-QPGW) calculations are used to calculate the electronic properties of α-Si3N4 and β-Si3N4, as well as α-SiO2 (quartz). The optical properties are evaluated by solving the Bethe-Salpeter equation in the Tamm-Dancoff approximation. For quartz, the predicted dielectric function is in good agreement with experimental data, with the onset of absorption located about 1.2 eV below the direct quasiparticle gap. For Si3N4, the theoretical dielectric function is fairly structureless and the onset of absorption corresponds to an exciton with a binding energy of 0.6 eV. The calculated sc-QPGW data are compared to more approximate calculations using G0W0, GW0, and a local multiplicative potential V(r) designed to predict accurate one-electron band gaps. Although these calculations yield similar one-electron energies as the sc-QPGW approach, the bands are too narrow, leading to a “compressed” optical spectrum with too small excitation energies at higher energies. Finally, we report the absolute shifts of the conduction- and valence-band edges in silicon nitride and silicon to facilitate the prediction of band alignments at silicon/silicon-nitride interfaces.