Calculations of F-19 magnetic shielding in various materials are presented. In calculations on gas-phase molecules, the variation of magnetic shielding with the amount of Hartree-Fock exchange (HFX) in the functional demonstrates that excellent agreement with experiment is obtained with an admixture of 50%, here denoted PBE0 (50%). Calculations at the PBE, PBE0 (25%), and PBE0 (50%) levels on 10 crystalline organofluorines and 15 crystalline inorganic fluorides, in which a cluster ansatz is used to model the lattice environment, were performed. For fluorine-containing aromatics, increasing the admixture of HFX results in the prediction of larger magnetic-shielding spans, whereas increasing the admixture of HFX in calculations for CFCl3 decreases the span. In calculations of F-19 magnetic shielding of the inorganic fluorides, the use of sufficiently large clusters of inorganic fluorides results in accuracies similar to those calculated for the organofluorines. Relativistic effects on the magnetic shielding of inorganic fluorides, modeled with ZORA at both the scalar and spin-orbit levels, are dominated by the scalar terms that increase the shielding of most F-19 sites over the non-relativistic results. These effects appear to scale with the atomic number of the cation. For most elements of the sixth row (Cs, Ba, La, and Pb), the scalar relativistic contribution to the magnetic shielding is in the range of 20-77 ppm. For elements of group XII (Zn, Cd, and Hg) bonded to fluorine, the scalar relativistic contribution results in deshielding of the F-19 site.