Nuclear magnetic resonance (NMR) is a powerful spectroscopic technique that is sensitive to the local atomic structure of matter. Computational predictions of NMR parameters can help to interpret experimental data and validate structural models, and machine learning (ML) has emerged as an efficient route to making such predictions. Here, we systematically study graph-neural-network approaches to representing and learning tensor quantities for solid-state NMR -- specifically, the anisotropic magnetic shielding and the electric field gradient. We assess how the numerical accuracy of different ML models translates into prediction quality for experimentally relevant NMR properties: chemical shifts, quadrupolar coupling constants, tensor orientations, and even static 1D spectra. We apply these ML models to a structurally diverse dataset of amorphous SiO$_2$ configurations, spanning a wide range of density and local order, to larger configurations beyond the reach of traditional first-principles methods, and to the dynamics of the $α\unicode{x2013}β$ inversion in cristobalite. Our work marks a step toward streamlining ML-driven NMR predictions for both static and dynamic behavior of complex materials, and toward bridging the gap between first-principles modeling and real-world experimental data.