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Cavity optomechanics offers significant reduction in noise and drift for inertial sensing devices by providing high signal-to-noise displacement sensing. Strong coupling between mechanical motion and optical resonances such as whispering gallery mode resonances has been shown to detect displacements at the femtometer scale. By using a photonic integrated circuit (PIC) ring resonator to detect the motion of a micro-electro-mechanical systems (MEMS) structure as it moves within the optical evanescent field, sensitivities 100-10,000x better than existing low-cost inertial sensors can be achieved. To design optimised accelerometers and vibratory gyroscopes, accurate finite element simulations of the PIC resonators are required to match the sophistication of MEMS modelling. We describe comparisons between frequency domain methods and 2D finite-difference time-domain (FDTD) methods for silicon ring resonators. As a demonstration of our working principle, we show experimental data where we measure the motion of a mechanical cantilever. We also characterise the thermo-optic induced shifting of the ring resonator resonance by measuring this effect, showing good agreement with FDTD simulations.