  We consider a nonlinear microcavity separating a waveguide channel into two
parts so as the coupling between them is possible only due to the resonant
properties of the microcavity. We provide a rigorous derivation of the
equations used in the phenomenological coupled mode theory for such systems.
This allows us to find the explicit formulas for all fitting parameters such as
decay rates, coupling coefficients and characteristic intensities in terms of
the mode profiles. The advantages of using the semi-analytical approach are
discussed, and the accuracy of the results is compared with the strictly
numerical methods. A particular attention is paid to multilayered structures
since they represent the simplest realization of on-channel microcavities.
