© 2020 Elsevier B.V. In order to investigate the formation and evolution of galaxies, stars and planetary systems, it is necessary to carry out astronomical observations in the far-infrared portion of the electromagnetic spectrum. Missions such as the Herschel Space Observatory (European Space Agency) have already completed observations in this region with great success. Proposed high resolution spectrometer instruments such as SAFARI (a joined European/Japanese (ESA/JAXA) proposal as part of the SPICA mission), aim to build upon the work of previous missions by carrying out observations in the 1.5–10 THz band with unprecedented levels of sensitivity. Spica (SPace Infrared telescope for Cosmology and Astrophysics) is currently a candidate mission as part of ESA's Cosmic Vision 2015–2025. Future far-IR missions must realise higher levels of sensitivity, limited only by the cosmic microwave background. One solution in achieving these sensitivity goals is to use waveguide coupled Transition Edge Sensor (TES) detectors, arranged in a densely packed focal plane. Additionally, multi-mode pixels can be used in order to maximise the optical throughput and coupling while still defining a definite beam shape. For the SAFARI instrument multimoded horns coupling into integrating waveguide cavities that house the TES detectors and associated absorbing layer are envisioned. This represents a significant technological challenge in terms of accurate manufacture tolerances relative to the short wavelength, however in the case of the SAFARI instrument pixel much work has already been carried out, with prototype pixels having undergone extensive testing at SRON (Space Research Organisation of the Netherlands) Groningen. In order to fully characterise the experimental results, it is necessary also to carry out comprehensive electromagnetic modelling of these structures which is also computationally intensive and requires novel approaches. These waveguide structures (horn and cavity) are typically electrically large however, and so analysis techniques using commercial finite element software prove inefficient (particularly as the structures are multimoded). The mode-matching technique with new analytical features offer a computationally efficient and reliable alternative to full electromagnetic solvers, and in this paper we outline the additions to this technique that were necessary in order to allow typical SAFARI far-infrared pixels to be modeled, including the complete optical coupling calculation of the measurement test setup at SRON and the inclusion of the free space gap within the horn antenna and the integrating cavity. Optical coupling efficiencies simulated using this developed technique show excellent agreement with the experimental measurements.