The paper is concerned with fast and robust contact detection methods for arbitrary ellipsoids. An iterative procedure, namely the Levenberg-Marquardt method, based on the common normal concept for parametric ellipsoids, is employed together with an implementation of the widely used GJK algorithm for comparison. The performance and accuracy of both are analysed and compared to each other on the basis of two test sets, each containing a total of 70 000 pairs of prolates or oblates. Emphasis is placed on the specific error measure relating the iterative solution to the exact one, which was chosen to be the maximum angle between the normal vector and the distance vector between two ellipsoids. The results indicate increased performance when using the Levenberg-Marquardt method over the GJK algorithm with no loss of accuracy.