A study of the electrodynamical properties of open coaxial cylindrical resonators using a partially conical inner rod is made along with experimental verification. On the basis of a geometrical criterion for the occurrence of high-Q resonances, it turns out to be possible to discriminate certain classes of TE modes by keeping to a minimum value their diffrationQ factors. In particular, for an especially designed cavity only TE0.2 and TE1.3 modes appear to have strong resonance in the 6 · 14GHz range as a result of the action of the coaxial insert.