Solid-state Mo-95 NMR spectroscopy is shown to be an efficient and effective tool for analyzing the diamagnetic octacyanomolybdate(IV) anions, Mo(CN)(8)(4-), of approximate dodecahedral, D-2d, and square antiprismatic, D-4d, symmetry. The sensitivity of the Mo magnetic shielding (sigma) and electric field gradient (EFG) tensors to small changes in the local structure of these anions allows the approximate D-2d and D-4d Mo(CN)(8)(4-) anions to be readily distinguished. The use of high applied magnetic fields, 11.75, 17.63 and 21.1 T, amplifies the overall sensitivity of the NMR experiment and enables more accurate characterization of the Mo sigma and EFG tensors. Although the magnitudes of the Mo sigma and EFG interactions are comparable for the D-2d and D-4d Mo(CN)(8)(4-) anions, the relative values and orientations of the principal components of the Mo sigma and EFG tensors give rise to Mo-95 NMR line shapes that are significantly different at the fields utilized here. Quantum chemical calculations of the Mo sigma and EFG tensors, using zeroth-order regular approximation density functional theory (ZORA DFT) and restricted Hartree-Fock (RHF) methods, have also been carried out and are in good agreement with experiment. The most significant and surprising result from the DFT and RHF calculations is a significant EFG at Mo for an isolated Mo(CN)(8)(4-) anion possessing an ideal square antiprismatic structure; this is contrary to the point-charge approximation, PCA, which predicts a zero EFG at Mo for this structure.