This thesis focuses on EM (electromagnetic) modelling methods for simulating the behaviour of receivers and detectors for far-IR (far-infrared) astronomy and CMB (cosmic microwave background) applications, toward an optimum design for SAFARI (the Spica Far-Infrared Instrument) on the proposed space based telescope SPICA (Space Infrared Telescope for Cosmology and Astrophysics). The computational methods required for modelling SAFARI-like receivers are described, and sophisticated conical waveguide mode matching theory is derived. Generic far-IR systems are investigated, including analysis of SAFARI-like multi-mode feed horns, and the absorber coupled superconducting TES (transition edge sensor) bolometers that are typically used in far-IR receivers. Special attention is given to the integrating cavity backshorts that serve to increase pixel efficiency, and new designs for improved cavity geometries, which provide high coupling between the detector and the incoming signal while reducing cavity losses and crosstalk, are presented. Where more than one simulation approach is employed for a particular problem, the agreement between the results served to mutually validate the approaches. Where necessary, experimental measurements were carried out for verification of the simulations, and the corresponding results are presented. The results of a measurement campaign carried out at SRON (Netherlands Institute for Space Research) during an extended visit during the summer of 2013 are presented, where a SAFARI-like horn antenna was characterised in terms of its frequency dependent throughput at THz (terahertz) frequencies. A series of cavity mounted absorber measurements are also described, where the detector components are appropriately scaled up in size to suit the frequency range of the in-house VNA (vector network analyser) system at NUIM (National University of Ireland, Maynooth). The main drivers for the work presented in this thesis were two Technology Research Programmes, both commissioned by ESA (European Space Agency).