Si-29 and P-31 magnetic-shielding tensors in covalent network solids have been evaluated using periodic and cluster-based calculations. The cluster-based computational methodology employs pseudoatoms to reduce the net charge (resulting from missing co-ordination on the terminal atoms) through valence modification of terminal atoms using bond-valence theory (VMTA/BV). The magnetic-shielding tensors computed with the VMTA/BV method are compared to magnetic-shielding tensors determined with the periodic GIPAW approach. The cluster-based all-electron calculations agree with experiment better than the GIPAW calculations, particularly for predicting absolute magnetic shielding and for predicting chemical shifts. The performance of the DFT functionals CA-PZ, PW91, PBE, rPBE, PBEsol, WC, and PBE0 are assessed for the prediction of Si-29 and P-31 magnetic-shielding constants. Calculations using the hybrid functional PBE0, in combination with the VMTA/BV approach, result in excellent agreement with experiment. (C) 2016 Wiley Periodicals, Inc.