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The film mode matching method for rigorous vectorial field analysis of circular microresonators and bent optical waveguides is described in detail. Immittance formulation is used to assure high numerical stability. Problems with the evaluation of cylindrical functions of complex order in the transition region and their cross products have been satisfactorily solved, which makes the method reliable and accurate. Results of two commercial mode solvers are used for benchmarking. The importance of vectorial modeling of microresonators is demonstrated by a numerical example.