Radar systems seek to detect targets in some search space (e.g. volume of airspace, or area on the ground surface) by actively illuminating the environment with radio waves. This illumination yields a return from targets of interest as well as highly reflective terrain features that perhaps are not of interest (called clutter). Data adaptive algorithms are therefore employed to provide robust detection of targets against a background of clutter and other forms of interference. The adaptive matched filter (AMF) is an effective, well-established detection statistic whose exact probability density function (PDF) is known under prevalent radar system model assumptions. Variations of this approach, however, lead to tests whose PDFs remain unknown or incalculable. This project will study the effectiveness of saddlepoint methods applied to approximate the known pdf of the clairvoyant matched filter, using MATLAB to complete the numerical calculations. Specifically, the approximation was used to compute tail probabilities for a range of thresholds, as well as compute the threshold and probability of detection for a specific desired probability of false alarm. This was compared to the same values computed using the known exact PDF of the filter, with the comparison demonstrating high levels of accuracy for the saddlepoint approximation. The results are encouraging, and justify further study of the approximation as applied to more strained or complicated scenarios.