We have investigated the dielectric properties of thin layers of five oxides of transition metals (Ta 2 O 5 , HfO 2 , ZrO 2 , (ZrO 2 ) 0.91 (Y 2 O 3 ) 0.09 , and Sn 0.2 Zr 0.2 Ti 0.6 O 2 ) sputtered from ceramic targets at different pressures. We find that layers deposited at low pressure behave as expected from literature, whereas layers deposited at high pressure all exhibit an anomalous dielectric response similar to that reported for the so-called ''colossal'' dielectric constant materials. The characterization of the thickness, frequency, and temperature dependence of the capacitance, as well as the comparison of film properties before and after annealing show that the anomalous dielectric response is due to quenched-in vacancies that act as dopants and cause the insulating layers to behave as semiconductors. An increase in quenched-in vacancies concentration with sputtering pressure results in a transition from normal to anomalous dielectric response and gradual increase in layer conductivity. In contrast, the refractive index does not depend on sputtering pressure. This observation indicates the possible application of these materials as transparent coatings with a tunable electrical conductivity.