This work discusses an issue caused by omitting the fourth-order zero-field splitting (ZFS) terms in the analysis of random-orientation EPR spectra. Eu(II)-doped strontium aluminates were employed as a model system of the S-state lanthanoid ions, which have relatively large second-rank ZFS components, comparable to the conventional X-band microwave energy. The initial estimation of second- and fourth-rank ZFS components was acquired uniquely from the W-band spectrum based on a perturbation treatment of the spin Hamiltonian, and they were refined by a hybrid-eigenfield simulation approach. A parallel simulation of the X- and W-band spectra with the refined parameters reasonably reproduced both the observed spectra. The reliability of the parameters was also verified by reproducing the off-principal-axis extra lines arising from the M-S = 1/2 <----> 1/2 transition observed in the W-band spectrum. By comparison with an analysis based on the spin Hamiltonian omitting the fourth-order terms, it was concluded that omitting these terms results in an erroneous determination of the rhombic parameter (E) of the second-rank ZFS tensor. The obtained reliable second-rank ZFS tensors enabled us to invoke the superposition model, determining their principal-axis orientation. This is the first report of such relative orientation determined for Eu(II)-doped strontium aluminates.