Several RF and microwave radiating devices, such as horn antennas, Fabry–Perot cavity antennas, and aperture-fed focusing devices, are excited through rectangular waveguides. The impedance matching of the overall system (from the waveguide feed to the radiating aperture) is a task of crucial importance that is often addressed by means of brute-force parameter-sweep full-wave analyses or blind optimization algorithms. In both cases, a significant amount of memory and time resources are required. For this purpose, we propose here a simple, yet effective solution, which only requires a single full-wave simulation and a semi-analytical procedure. The former is used to retrieve the antenna input impedance at the end of the waveguide port excitation. The semi-analytical procedure consists in a transmission-line equivalent circuit that models two waveguide discontinuities (namely two capacitive irises) within the …