Is the electrical conductivity only measurable in aqueous solutions?
Did you look into ionic liquids? Also in ionic complexes like poly (ethylene oxide)? For instance, look into these references: 


P. V. Wright, Electrical conductivity in ionic complexes of poly(ethylene oxide), Polymer International, 1975, 7(5), 319-327 (https://doi.org/10.1002/pi.4980070505).
Q.-G. Zhang, S.-S. Sun, S. Pitula, Q.-S. Liu, U. Welz-Biermann, J.-J. Zhang, Electrical conductivity of solutions of ionic liquids with methanol, ethanol, acetonitrile, and propylene carbonate, J. Chem. Eng. Data, 2011, 56(12), 4659–4664 (https://pubs.acs.org/doi/abs/10.1021/je200616t).