Cluster-based calculations of Te-125 magnetic-shielding tensors demonstrate that inclusion of spin-orbit effects is necessary to obtain the best agreement of theoretical predictions with experiment. The spin-orbit contribution to shielding depends on the oxidation state and stereochemistry of the Te-125 site. Comparison of the performance of various density functionals indicates that GGA functionals behave similarly to each other in predicting NMR magnetic shielding. The use of hybrid functionals improves the predictive ability on average for a large set of Te-125-containing materials. The amount of Hartree-Fock exchange affects the predicted parameters. Inclusion of larger Hartree-Fock exchange contributions in hybrid functionals results in larger slopes of the correlation between calculated magnetic-shielding and experimental chemical-shift principal components, by 10-15% from the ideal value.