Scanning thermal microscope based DC measurements of local thermal conductivity are relevant to insulating (<20 W m-1 K-1) materials only. We aim at using the 3omega method to enhance the sensitivity of the device to a larger range. In this paper we present both a thermal model and experimental results from the calibration procedure to study the thermal behaviour of stand-alone probes. The two approaches provide data in very good agreement on the full measured frequency domain. Several geometric and thermal parameters are deduced from the comparison. Those quantities are key inputs for future heat transfer modelling of the tip-sample contact.