Total Internal Reflection Microscopy (TIRM) is an experimental technique that allows the potential energy profile of a colloidal particle above a plate to be determined from the particle's observed Brownian motion. We have used Brownian Dynamics (BD) simulations to numerically simulate TIRM experiments. We show that a careful treatment of the position dependence of the colloidal particle's mobility near the plate is vital to performing realistic simulations. These simulations enable us to systematically study the effect of experiment duration, data sampling methods, and physical parameters of the suspended colloid on the accuracy of potential energy profiles determined via TIRM. We also present an analytical theory to predict the range of energies reliably probed by TIRM experiments. This theory provides simple guidelines for the design and optimization of future TIRM experiments. Finally, we have used BD simulations to investigate the use of radiation pressure and the effects of experimental noise in TIRM experiments.