In this paper, a method is given for calculating the phase constant of waveguide structures used in integrated optics. As a basis, the Rayleigh-Schrödinger perturbation approach of first and second order is applied. Due to the knowledge of the limiting behavior of the phase constant at high frequencies, an appropriate functional approximation is derived and combined with the mode-matching procedure to reduce the numerical effort. Results are obtained for the HE00mode and EH00mode. A comparison with more accurate numerical techniques, as the method of lines for instance, shows a good correspondence.