The interface between empty and dielectric-loaded lossless waveguides is discussed in terms of three independent measurable quantities. A mode-matching technique is used to obtain an equivalent-circuit representation of the junction, when only the dominant mode propagates in each waveguide. The circuit has the form of two equivalent transmission lines, which describe the two waveguides, and a 2-element network, which describes the effect of the interface. It is shown that this is the only meaningful and useful representation, and that a unique value of the normalised equivalent characteristic admittance of the inhomogeneous waveguide can thus be determined for any loading configuration. This admittance is shown to be not generally proportional to the wave admittance, even when the latter can be defined. In most practical situations, where only one mode may propagate in each waveguide, the effect of the interface can be neglected and matching can be achieved on the basis of this characteristic admittance alone. Computed values of the normalised equivalent-circuit elements and characteristic admittances are given for both E-plane and H-plane loading over a wide range of parameters.