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Single crystals of BaWO4, BaWO4: 0.5 at. % Ce; BaWO4: 1 at. % Ce; BaWO4: 0.5 at. % Ce, 1 at. % Na; and BaWO4: 1 at. % Ce, 2 at. % Na were grown from an inductively heated iridium crucible by the Czochralski method on a Malvern MSR4 puller. They were investigated using Electron Paramagnetic Resonance (EPR) spectroscopy at helium temperatures. One isolated center of high (D2d or S4) symmetry was found and two or more other centers of lower symmetry were identified, depending on crystal doping. From the fitting using the EPR-NMR program, the following parameters of g-matrix for the high symmetry center were found: gx = 1.505, gy = 1.505, and gz = 2.731. The linewidth vs. temperature revealed an increasing exponential tendency with increasing temperature. It showed one phonon at the lower temperatures and a Raman + Orbach effect at the higher temperatures. Radioluminescence and pulse height spectra showed rather poor scintillation properties, without any contribution from cerium emission.