Conductive plastics have become an alternative to traditional metallic cabinets to shield boxes from electromagnetic interferences. These materials allow a wide range of conductivities that can satisfy any particular design. A design with an outer metallic layer and an inner layer of conductive dielectric can obtain advantages from both materials. In this paper the damping of resonances in enclosures with an aperture through conductive dielectrics is optimized by means of Genetic Algorithms with the aid of a three dimensional simulation tool. Genetic Algorithms are a general purpose optimization technique widely used in the last years for electromagnetic design. The relationship between obtained solutions and skin depth parameter is shown in order to help in design procedures.