The primary focus of this thesis is the re-formulation and extension of traditional mode-matching methods, and the development of the software package SCATTER-TNG (S-TNG) to incorporate them. The foundations of this software are built on the legacy of mode matching routines developed by the Terahertz Group at Maynooth University. This new adaptation aims to enable continued contributions to the design, analysis, and efficient characterisation of the sensitive pixel (feed, cavity, and absorber) structures of future far-infrared instruments. Contemporary waveguide technologies increasingly rely on the exploitation of multi-moded behaviour and operation in higher frequency bands. In these scenarios a more comprehensive approach is required to correctly predict their behaviour as the assumption of ideal surfaces may no longer be entirely valid. In S-TNG, the fundamental description of fields within waveguides and at discontinuities relies on auxiliary vector potentials rather than their measurable electric and magnetic field quantities. Moreover, the necessary mode matching integrals are derived in terms of contour rather than surface integrals. The reformulations offer an alternative, somewhat more flexible, mathematical representation of the mode matching problem. Furthermore, mode matching methods are extended to allow for non-PEC (Perfect Electrically Conductive) treatment of the boundary walls. These non-PEC boundary walls consider mechanisms for loss which are generally not included in the modal analysis of guide structures. In particular, losses may manifest themselves more significantly in multi-moded structures, as field distributions for increasing higher order modes are localised to a greater extent at the boundary walls. The motivation for this body of work stemmed from ESA contracted work focused on “New Technology High Efficiency Horn Antennas for Cosmic Microwave Background Experiments and Far-Infrared Astronomy” – fulfilling the requirement to model multi-moded pixel devices for THz space instruments. This included the ability to easily model arbitrary shaped absorbers in an infinitely thin absorber layer model achieved via the contour integral implementation. The software tools developed have since been applied to the design and analysis of some proposed pixel and feed designs for the SPICA/SAFARI instrument. In particular, there is great interest in the non-PEC treatment of the boundary walls for the analysis of prototype designs.