Asymptotic eigenvalue distribution functions have been used in physics to approximate the actual frequency distribution of modes in resonant cavities. Certain versions of these formulas have been incorrectly applied to microwave cavity problems in engineering. A brief review of the relevant physics literature is presented along with some of the important results which should be used in engineering calculations. Also presented are the results of experimental measurements (on rectangular cavities), which verify the physical theory at microwave frequencies. Several features of the exact and approximate mode distributions become evident from this study, and these are discussed with respect to microwave cavity design.