A numerical solution for electromagnetic coupling to a perfectly conducting body of revolution with a loss-free homogeneous material region is developed here. The material region is exposed by a rotationally symmetric aperture in the conducting body. Application of the equivalence principle introduces an unknown electric current on the surface of the conducting body, and both an unknown equivalent electric current and an unknown equivalent magnetic current in the aperture. These currents satisfy the integral equations obtained by annihilating the tangential components of the electric field on the surface of the conducting body and by enforcing continuity of the tangential components of the electric and magnetic fields across the aperture. These integral equations are solved numerically by means of the method of moments.