In the present work, the electrical conductivity of a molten slag in the Al2O3-CaF2-CaO (slags for the electro slag remelting / ESR process) system is measured using different electrode arrangements and evaluation methods. A two-electrode coaxial setup, as well as a four-electrode van der Pauw setup are implemented, using materials resistant to the slag. By acquiring one (coaxial case) or more (van der Pauw) impedance spectra per immersion depth, extracting the electrolyte resistance using equivalent circuit approximation, and accurately measuring the immersion depth difference, the conductivity is determined using cell constants and mathematical-analytical models. The availability of impedance spectroscopy will enable the gain of new insights in the field. In preparation for conductivity determinations on slags containing iron oxide, considerations are being made with regard to suitable electrode and crucible materials. The results of measurements on ESR slag with the coaxial arrangement differ greatly from those found with the van der Pauw method. Based on these results and the experience gained from the experiments, a list of criteria for reproducible conductivity determinations on mineral melts is created. Finally, an outlook is given on the importance of ionic and electronic conduction phenomena for steel metallurgy and on further developments regarding potentiostatic activity measurements.