The structures of several fluoroscandate compounds are presented here using a characterization approach combining powder X-ray diffraction and solid-state NMR The structure of K5Sc3F14 was fully determined from Rietveld refinement performed on powder X-ray diffraction data. Moreover, the local structures of NaScF4, Li3ScF6, KSc2F7, and Na3ScF6 compounds were studied in detail from solid-state F-19 and Sc-45 NMR experiments. The Sc-45 chemical shift ranges for six- and seven-coordinated scandium environments were defined. The F-19 chemical shift ranges for bridging and terminal fluorine atoms were also determined. First-principles calculations of the F-19 and Sc-45 NMR parameters were carried out using plane-wave basis sets and periodic boundary conditions (CASTEP), and the results were compared with the experimental data. A good agreement between the calculated shielding constants and experimental chemical shifts was obtained. This demonstrates the good potential of computational methods in spectroscopic assignments of solid-state Sc-45 NMR spectroscopy.