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OrthoMode Transducers (OMTs) play a fundamental role in the implementation of antennas for dual polarization transceivers and their design is critical for achieving good performances. We describe an efficient electromagnetic simulator for the Computer Aided Design (CAD) and Optimization of OMTs which employs two different types of full-wave electromagnetic analysis (i.e. the generalized scattering matrix and the generalized admittance matrix) and a topological optimization of the overall OMT structure. This design tool has been successfully employed in the realization of several OMTs for various satellite applications. Favorable measured and computed electrical performances of all breadboards prove the great flexibility and accuracy of the proposed design tool.