Many estimators and tests are of the form of a ratio of quadraticforms in normal variables. Excepting a few very special cases littleis known about the density or distribution of these ratios,particularly if we allow for noncentrality in the quadratic forms.This paper assumes this generality and derives saddlepointapproximations for this class of statistics. We first derive andprove the existence of an exact inversion based on the jointcharacteristic function. Then the saddlepoint algorithm is appliedand the leading term found, and analytic justification of theasymptotic nature of the approximation is given. As an illustrationwe consider the calculation of sizes and powers ofF-tests, where a new exact result is found.