Both the orthogonal modal series method and the high-frequncy asymptotic evaluation method are used to analyse the mutual coupling between two apertures on a perfectly-conducting sphere. The computational formulas of mutual coupling are derived. The numerical techniques of some special functions are discussed and the numerical results are given. The comparison between the two methods shows that each of them has its advantages and shortcomings. The accuracy of the asymptotic evaluation method is tested. And the mutual coupling between a pair of rectangular slots on a sphere VS. their relative location parameters is investigated.