A theoretical model is presented for a coaxial-line probe to rectangular-waveguide transition for the case where the probe is dielectrically sheathed and extends part of the way into the waveguide. Comparison of theoretical with experimental results demonstrates that the model is very accurate. The model is used to perform a bandwidth investigation of both sheathed and unsheathed probe transitions to gain insight into the effects of various junction parameters. It is found that the electrical size of the coaxial-line aperture in the waveguide plays a significant role in the overall bandwidth performance of the transition, and in many cases the bandwidth performance may be enhanced by offsetting the location of the junction from the centre of the waveguide or by dielectrically sheathing the probe in the waveguide.