The nature of magnetism in 10% Cu-doped ZrO2, TiO2, MgO, SiO2, and Al2O3 is investigated using superconducting quantum interference device magnetometry and electron magnetic resonance (EMR). The doping was done by the incipient wetness impregnation technique. X-ray diffraction studies showed the presence of some CuO notably in TiO2, SiO2, and Al2O3. However, EMR yielded typical Cu2+ spectra in all the samples, resulting from some doping. Magnetic field (H) and temperature (T) dependences of the magnetization (M) show only paramagnetism in these oxides in contrast to ferromagnetism with Tc=380 K observed in Cu/ZnO. Concentrations x of Cu2+ doped into the oxides are determined from the M vs T and M vs H data, showing Cu/ZrO2 with the largest x and hence largest magnetization.