Bolometric integrating cavities have been used with great success in previous far-infrared space missions, and are planned for extensive use in future missions where ever increasing sensitivity is required. It is critical for the purposes of design and the interpretation of results that these systems are thoroughly understood and optically characterised fully. Such systems, for manufacturing and mechanical reasons, may contain free space gaps between the feed horn antenna and the integrating cavity, and so it is necessary to include the effect of these waveguide openings in simulations. Since these pixels are electrically large, it is more feasible to model them by using the computationally efficient mode-matching approach. In this paper we discuss the elements required to model such pixels within the mode-matching approach and apply it to a typical pixel containing a free space gap, based on an experimental Transition Edge Sensor (TES) cavity waveguide pixel at SRON Groningen.