We report the theoretical F-19 NMR shielding tensor magnitudes and orientations for a series of fluoroaromatic species, together with a comparison with experimental results. We discuss results for Hartree-Fock (HF) and second-order Moeller-Plesset theory (MP2) geometry optimized structures and HF-gauge including atomic orbitals (HF-GIAO), sum over states-density functional theory-independent gauges for localized orbitals (SOS-DFT-IGLO) and MP2-GIAO shielding calculations, for several basis set arrangements. In general, MP2 and DFT methods show few improvements over HF methods, at the expense of time (MP2) and accuracy (MP2 and DFT). Pure density functionals overestimate the tensor breadths (spans), an effect that is only partially offset by use of hybrid exchange correlation functionals. HF-GIAO methods in general give good overall predictions of F-19 shielding tensor elements. In the case of potassium tetrafluorophthalate, we also demonstrate that use of the charge field perturbation-IGLO technique provides accurate shielding tensor elements, as well as accurate shielding tensor orientations. We also report the calculation of the shielding derivatives, partial derivative sigma (ii)/partial derivativer, for the F-19 nucleus in fluorobenzene (and HF) and the H-1 nucleus in benzene. Surprisingly, the derivative along the C-F bond axis (partial derivative sigma (22)/partial derivativer) is quite large, 460 ppm Angstrom (-1), unlike that expected and found in HF, or in benzene, indicating a strong p-orbital interaction with the benzene ring. The F-19 shielding tensor results are thus quite sensitive to the actual bond lengths employed (derived from geometry optimizaitons), with MP2 optimization permitting the best accord with experiment. Overall, MP2 optimization and HF-GIAO shielding tensor calculations were found to give the best results, consistent with previous isotropic chemical shift/shielding results.