A brief review of existing diagnostic methods allowing to determine the interface position and velocity during the solidification of liquid metals and semiconductors is first presented. We then show that a recently proposed electronic design can be used to measure the electrical resistance of the sample with a very high accuracy: the peak to peak noise on the signal is significantly lower than 1 muOmega. In the tin-based system used in our investigations, this amounts to a resolution in terms of solid-liquid interface position of the order of a few micrometers. The experimental results show that our resistance measurement technique allows to identify the thermal lag of the furnace in the initial solidification stage, as well as a transfer function between actual and imposed interface fluctuations.