The 𝑔 factors and the ligand superhyperfine parameters $A'$ and $B'$ for Ni³⁺ in KMgF₃, CsCaF₃ and RbCaF₃ are theoretically studied from the formulas of these parameters for a 3d⁷ ion under octahedral environments in the weak field scheme. The unpaired spin densities for the fluorine 2s, 2p$_{\sigma}$ and 2p$_{\pi}$ orbitals are quantitatively determined from the molecular orbital and configuration interaction coefficients based on the cluster approach. The calculated results show good agreement with the experimental data, based on only one adjustable parameter (i.e., the proportionality factor 𝜌 related to the ligand s- and p-orbitals). The superhyperfine parameters for the axial and planar ligands in RbCaF₃:Ni³⁺ are satisfactorily interpreted from the different impurity–ligand distances due to the elongation of the ligand octahedron during cubic-to-tetragonal phase transition.