Topography simulations are widely used in the microelectronics industry to study the evolution of surface profiles during such processes as deposition or etching. Comparisons between simulations and experiments are used to test proposed transport and chemistry models. The method used to move the surface (the moving algorithm) should not interfere with this testing process; i.e., it should not introduce artifacts. The reference method, shown to be accurate by several groups in many studies, is conservation law based "front tracking." Level set approaches are being increasingly used, largely for their robustness to topological changes. They have not been tested against front tracking to determine their accuracy. In this article, we present guidelines on the use of level set methods for two-dimensional surface evolutions as commonly used. Specifically, we deal with two major issues with level set algorithms: the need for "extension velocities" and the rounding of sharp corners due to contouring. We also deal with a specific approach to velocity extension that is called "fast marching." Although all methods discussed can provide the same results within the limit of small enough time steps, we demonstrate that our proposed "Riemann based" extension velocities can improve overall simulation efficiency by approximately a factor of 2, depending upon the complexity of the process being simulated. We also show that as the grid size used in the level set method decreases, extracted surface profiles can approach those calculated by front tracking, and hence to experiments.