Inverse modelling methods are receiving significant interest, due to their simplicity and ease of use in the design of modern microwave components. This study investigates and further develops the technique of numerical time-reversal, in the context of automated component design, for modelling metal waveguide devices. The thesis demonstrates that time-reversal methods suffer from temporal truncation, evanescent wave decay and significant computational resource requirements and will investigate different methods to solve these problems. In order to reduce the runtime, the use of Prony’s method for temporal extrapolation of a discrete waveform is proposed. Lossy materials are investigated, with particular attention given to the loss of modal content from the reverse model due to material loss present in the forward phase of the time-reversal process. The memory and time requirements of a successful time-reversal design simulation are significant. Temporal, spatial and modal filtering are used to minimise the computational demands of time-reversal. Further, in order to accelerate convergence of the time-reversal design process, a number of linear acceleration methods are developed, notably successive over relaxation, conjugate gradients and generalised minimal residual. A convergence acceleration factor of two is achieved. It is shown that local evanescent content around optimised scattering elements is not always captured by the time-reversal process, and is dependant upon the component order, numerical sampling and machine precision. Internal mirrors are developed which capture the fast decaying fields around the metal features of a designed component and further increase the accuracy and speed of the time-reversal convergence. Their use for higher order component design is shown to be paramount in achieving convergence. Further, combined with the linear acceleration methods, the capture of local evanescent content is shown to greatly improve the viability of the time-reversal technique to practical microwave component design. The time-reversal methodology is implemented using the numerical transmission-line modelling (TLM) method for transverse magnetic polarisation in two-dimensions. A brief examination of the three-dimensional time-reversal using the symmetrical condensed TLM node is also given.