I am afraid it might be a late response to you, but maybe it might help others in the future.
There are several ways for determining the proton conductivity with Impedance Spectroscopy. For fuel cells, the most frequently used is the equation σ=L/(Z.A), where σ is the conductivity, L is the sample thickness, A is the electrode area and Z is the impedance value. The value of impedance used for this calculation is the resistance estimated from the intersection (at high-frequency) of the real axis (Z’) and the semicircle of the nyquist plot. You can find a good discussion about this topic in the following article (https://onlinelibrary.wiley.com/doi/10.1002/admi.201801146). Hope it helps you.