The increasing use of microstrip antenna arrays calls for a rigorous analysis of the coupling between antenna elements. In this paper a full wave analysis is presented to rigorously formulate the resonance of a coupled two circular disk resonator using the Vector Hankel Transform, together with the translational properties of the cylindrical harmonics. The matched asymptotic expansion approach is then used to asymptotically evaluate the resonant frequencies of the structure. The Galerkin moment method and a perturbative approach which can also be used to calculate the resonant frequencies are reviewed. The results obtained using these methods are compared with those of the matched asymptotic expansion approach developed in this paper. It is shown that the asymptotic matching approach provides significant saving in computation time and furthermore supplies simpler expressions for the resonant frequencies as compared to the Galerkin method and the perturbative approach.