In the analysis of mutual coupling in apertures on a convex surface, the surface field due to a magnetic dipole on a large conducting cylinder is an important canonical problem. Over the years a number of approximate asymptotic solutions have been described in the literature. In this paper the accuracy of five of the best solutions currently available is tested by comparing them with the exact modal solution. This comparison is accomplished by placing the modal solution in a more efficient form for numerical evaluation. From a study of four ray trajectories on cylinders of radius 1.5171 and four wavelengths it is concluded that two complementing solutions due to Boersma and Lee and the author have best overall accuracy. The former solution is most accurate near the source and in the paraxial region while the latter is best far from the source and off axis. The worst case errors observed for the test trajectories on the four wavelength cylinder were approximately 1 dB in magnitude and 3° in phase for the Boersma-Lee solution and 0.5 dB and 4°, respectively, for the author's solution. Generally the errors are considerably less than these values.