I'm not very sure but you could tell the extent of conductivity of the proton conductor by observing the ohmic resistance of your symmetric cell during EIS test since the major migration species is proton. To be more precise, you might take note of the thickness of your electrolyte.
For the first indication, to investigate if the material is proton conductive or not, a conventional acid-base titration approach can be used to determine the ion exchange capacity (IEC).
Briefly, the weighted dry sample is soaked in a known volume of NaCl solution for 24 h to exchange Na+ ions with H+ ions. Then, the liberated H+ can be estimated by titration against NaOH solution using phenolphthalein as the indicator.
The following equation calculated the IEC: 𝐼𝐸𝐶 = 𝐶𝑁𝑎𝑂𝐻 × 𝑉𝑁𝑎𝑂𝐻/ 𝑀𝑑𝑟𝑦 Where IEC is the ion-exchange capacity (meq g-1), VNaOH is the consumed titrant volume of NaOH solution (mL); C NaOH is the molar concentration of the titrant, and Mdry is the dry mass of the sample (g).
this technique can be used as an indication of the capability of the material for proton conductivity.
for an exact result, you can use in-plane or through-plane proton conductivity by an AC impedance technique using an electrochemical impedance analyzer.