An extension of the traditional mode-matching methods to consider non-PEC boundary walls is presented. These non-PEC boundary walls consider mechanisms for loss which are generally not included in the analysis of guide structures. In particular, these losses manifest themselves more significantly in multi-moded structures, as field distributions for increasing azimuthal order modes are localised to a greater extent at the boundary walls. This lossy mode-matching method is applied to a prototype M-band horn for the proposed SAFARI system. Here we attempt reconcile the measurement data with simulation results by considering the surface impedance of the guide walls due to the finite conductivity and surface roughness from the manufacturing process.