This thesis describes electromagnetic and optical modelling for three tele- scopes operating at GHz and THz frequencies: the Pickmere telescope, QUBIC and ALMA. Optical modelling was carried out using TICRA’s GRASP phys- ical optics software and also using a Gaussian beam mode model developed in Python. The electromagnetic modelling of corrugated horn antennas was carried out using Maynooth University’s existing mode-matching software ‘PyScatter’ and new code developed for this thesis called ‘NumCross’. The Pickmere radio telescope was simulated using Gaussian beam modes and also using GRASP physical optics. The two methods agreed to a high level of accuracy. This verified the accuracy of Gaussian beam mode analysis as a rapid, simplistic model of sequential mirrors in telescopes. A series of horns were developed for a potential ALMA combined band 4 and 5, and in particular the effects of different manufacturing constraints on horn performance were shown. A comparison was made between the in- house PyScatter routine and the industry standard HFSS software used by col- laborators in Manchester University. The programs largely agreed, with one difference caused by differing sensitivity to back-propagation of radiation. The QUBIC telescope makes use of an array of corrugated horn antennas manufactured using a platelet technique. The plates can incur lateral offsets due to alignment tolerances during manufacturing. These offsets cannot be modelled in PyScatter as it assumes cylindrical symmetry at platelet junctions. The NumCross routine was created, building on PyScatter, to allow the mod- elling of corrugated horns with laterally offset corrugations. The QUBIC horns were modelled as an example.