The electronic structure and magnetism of mixed-valence, host-guest polyoxovanadates {X@VO54} with diamagnetic (X =) ClO4- (Td, 1) and SCN- (C∞v, 2) template anions are assessed by means of two theoretical methods: density functional theory and effective Hamiltonian calculations. The results are compared to those obtained for another member of this family with X = VO2F2- (C2v, 3) (see P. Kozłowski et al., Phys. Chem. Chem. Phys., 2017, 19, 29767-29771), for which complementary data are also acquired. It is demonstrated that the X guest anions strongly influence the electronic and magnetic properties of the system, leading to various valence states of vanadium and modifying V-O-V exchange interactions. Our findings are concordant with and elucidate the available experimental data (see K. Y. Monakhov et al., Chem. - Eur. J., 2015, 21, 2387-2397).