A conical-tip probe for the measurement of permittivity is presented which retains many of the advantages of the normal plane probe including ease of sample preparation and moderate sample volume requirement, but which is mechanically better suited than monopole probes for the measurement of a wide range of biological materials since it does not promote free moisture regions resulting From cell rupture. The probe input admittance is found by modelling the probe as a short partially-sheathed monopole in free space and then a well-known antenna scaling theorem is used to determine the admittance and hence permittivity in the dielectric medium.