A new and comparatively small type of open-ended microwave applicators has been disclosed. They are for example suitable for transmission into and reception from contacting objects such as protruding human bodyparts for inhomogeneity detection by tomographic methods. The applicators according to the invention are of the dielectric-filled open-ended ridged rectangular TE10 type, with an insert filling the ridge and having a higher permittivity than the surrounding space. The shape of the insert can be as a frustrum pyramid towards the opening. The overall design promotes narrow beamwidths and minimises nearfields and surface wave excitation.