The relationship between the g-shift and the local structure of the Ce3+ paramagnetic center with axial symmetry were investigated for four BaWO4 single crystals doped with Ce and codoped with Na. Based on g-shift the displacements of Ce3+ ions are determined. The g-shift method yields displacements of impurity ions in good agreement with the superposition model (SPM) and the perturbation methods (PM) predictions. The structural analysis of the paramagnetic ions and its surrounding in the BaWO4 unit cell was also conducted.