This thesis is concerned with the application of electromagnetic modelling techniques to the analysis of horn antenna characteristics over the terahertz range, 0.1 THz to 5 THz. The mode matching technique based on a scattering matrix approach to describe beam propagation in both the forward and backward direction is applied to the analysis of conical and pyramidal horn antenna both single and multi-moded, in particular the multi-moded pyramidal horn antenna array of the SAFARI instrument - a far infrared imaging spectrometer to be launched onboard the future SPICA mission. A second electromagnetic method - the finite integration technique is applied to the analysis of simple waveguide structures and characteristics associated with them through commercially available package CST. Where appropriate a quasi-optical approach to the analysis is also applied for comparison and verification of the results, namely Gaussian beam mode analysis. The underlying theory behind these analytical techniques and their implementation is provided along with descriptions of software packages used in the analysis, these are μWave Wizard a commercially available software package based on the mode matching technique, CST Microwave studio commercially available software utilising the finite integration technique and SCATTER code developed at NUI Maynooth using the mode matching technique. Gaussian beam mode propagation using both Gauss-Laguerre and Gauss-Hermite mode sets is implemented by code written within the Mathmatica environment. The effectiveness of each method in its application to particular structures to obtain accurate and computationally feasible results is discussed. Particular effects inherent is quasi-optical systems, crosstalk and standing wave effects are analysed in addition in later chapters. These effects are analysed both experimentally using a vector network analyser and within appropriate computational models.