Thin films of zirconium oxide (ZrOx) and hafnium oxide (HfOx) were rf sputtered onto fused silica substrates in an oxygen rich argon environment. Pure zirconium and hafnium targets were used, and the oxygen partial pressure was varied to control the oxygen stoichiometry. Measurement of the EPR characteristics of the ZrOx films indicated two peaks corresponding to two orientations of the magnetic field. This anisotropic response suggested the films were polycrystalline with a preferred orientation. This was confirmed by XRD pole figures. The measured g-values for the ZrOx films were less than the free-spin g-value, indicating the defects corresponded to electron traps. It was further shown that the lower the oxygen partial pressure during deposition, the larger the EPR response, strongly suggesting the traps correspond to oxygen vacancies in ZrOx. Hafnium oxide thin films were also characterized by EPR. The EPR measurements indicated the presence of a single resonance peak, suggesting these films were polycrystalline without a preferred orientation or amorphous. XRD measurements confirmed that the HfOx films were amorphous. The g-value for these films was greater than that the free-spin value, indicating the presence of possibly self-trapped oxygen hole centers. These results will be discussed in the context of prior experimental and theoretical work on these systems.