The F-19 NMR chemical shieldings of solid-state alkaline-earth-metal fluorides MF2 (M = Be, Mg, Ca, Sr, Ba) and alkali-metal fluorides MF (M = Li, Na, K, Rb, Cs) were systematically studied by the gauge-independent atomic orbital (GIAO) method at the level of density functional theory (DFT). The 6-311+G(d) basis set was used for the inspected fluoride ion. The performance of the effective core potentials (ECP) of LanL2DZ and CRENBL basis sets for metal atoms were compared to 3-21G all-electron basis set. The role of d polarization functions for metal atoms is investigated. The results show that the clusters [FMg3F9](4-), [FM4F6](+) (M = Ca, Sr, Ba), and [FM6](5+) (M = Li, Na, K, Rb, Cs) used to model the bulk solids are reasonable The electrons in the next outermost shell of metal atoms have significant influence on the F-19 NMR calculations and should be treated as valence electrons together with the electrons in the outermost shelf, while die remaining electrons can be represented by the ECP of CRENBL basis set. When the CRENBL basis set (with ECP for core electrons) supplemented with two sets of d polarization functions was used for the metal atoms, the approach of locally dense basis sets can be used to successfully reproduce the F-19 shielding values. Since only the inspected resonant fluorine atom needs a high-grade all-electron basis set, it is a relatively inexpensive means of obtaining reliable shielding properties for the inspected species. In addition, the different exchange-correlation functional implemented in hybrid DFT method has a minor influence on the calculated shielding. Although all the calculated results are somewhat overestimated, the correlation coefficients and the slopes of the fitting lines between the theoretical predictions and experimental observations are close to unity, indicating the good agreement of the theoretical results to the experimental values.