Computational models for microwave power launching, propagation and absorption are described. Two methods are developed for the reconstruction, based on ray tracing data, of the power density that impinges on a surface. One of the methods allows treatment of rapid power density variations that occur when the ray tracing exhibits caustics. The models are applied to the analysis of experiments using 140 GHz free-electron-laser power injected into a high density plasma in the Microwave Tokamak Experiment.