In this work, the etching behaviour of reactively co-sputtered amorphous $Al_2O_3$ and polycrystalline $Y_2O_3$ films was investigated using an inductively coupled reactive ion etch system. In $Al_2O_3$ channel waveguides were fabricated with BCl3/HBr plasma and using a standard resist mask, while in $Y_2O_3$ channel waveguides were fabricated with Ar and using either a resist or sputter deposited $Al_2O_3$ mask layer. The etched structures in both materials exhibit straight sidewalls with minimal roughness and sufficient widths (down to 1.0 µm for $Al_2O_3$ and 1.4 µm for $Y_2O_3$) and etch depths (up to 530 nm for $Al_2O_3$ and 250 nm for $Y_2O_3$) for defining waveguides with strong optical confinement. Using the developed etch processes, single-mode ridge waveguides were fabricated in both $Al_2O_3$ and $Y_2O_3$ layers and additional losses introduced by etching, as determined by subtracting the known background losses of the un-etched films from the measured channel losses, were found to be low (< 0.5 dB/cm).