Is the electrical conductivity only measurable in aqueous solutions? I have been looking for other ways to measure it, but all I've found is through aqueous solutions. So I want to know if there's another way to do it, or why it isn't possible through other means.
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).