We report on the design and measurement of tellurium oxide microcavity resonators coupled to silicon bus waveguides on silicon photonic chips. The resonators are fabricated using a standard silicon photonics foundry processing flow in which the SiO₂ top-cladding is etched in a ring shape and aligned next to a silicon bus waveguide. The resulting microtrench is coated in a tellurium oxide film by reactive sputtering in a post-processing step to form the waveguiding layer of the resonator. A 100-μm radius trench with a 1115-nm-thick TeO₂ film is measured to have an internal Q factor of 0.9  ×  10⁵. Smoothing the etch wall surface with a fluoropolymer coating is shown to enhance the Q factor of several devices, with a trench coated in a 630-nm-thick TeO₂ film demonstrating a Q factor of 2.1  ×  10⁵ corresponding to 1.7-dB/cm waveguide loss. These results demonstrate a potential pathway toward monolithic integration of tellurite glass-based nonlinear and rare-earth-doped devices compatible with silicon photonics platforms.