The regularization of the integral equations for the solution of electromagnetic problems is discussed. The technique includes a semi-analytic inversion of the integral operator resulting in equation of the Fredholm second kind, which can be solved using numerical inversion. The procedure is employed through Riemann-Hilbert Problem technique for the electromagnetic problems that can be put into a dual-series equation form. An example of the method is described for the E-wave scattering from a cavity-backed aperture.