We describe a procedure for simulating the behavior of partially coherent submillimeter-wave antenna systems. The procedure is based on the principle that the second-order statistical properties of any partially coherent vector field can be decomposed into a sum of fully coherent, but completely uncorrelated, natural modes. Any of the standard electromagnetic analysis techniques-physical optics, geometrical theory of diffraction, etc.-can be used to propagate and scatter the modes individually, and the statistical properties of the total transformed field reconstructed at the output surface by means of superposition. In the case of modal optics-plane waves, Gaussian optics, waveguide mode matching, etc.-the properties of the field can be traced directly by means of scattering matrices. The overall procedure is of considerable value for calculating the behavior of astronomical instruments comprising planar and waveguide multimode bolometers, submillimeter-wave optical components, and large reflecting antennas.