To measure the conductivity of your LLZO+PEO polymer composite electrolyte film, the most reliable method is AC impedance spectroscopy (EIS). Sandwich your film between two blocking electrodes, optionally using silver paste for better contact. Apply a small AC voltage over a range of frequencies, measure the impedance response, and analyze the resulting Nyquist plot to determine the bulk resistance. Finally, calculate the conductivity using the film dimensions and measured resistance. Ensure consistent sample preparation, control environmental conditions, and repeat measurements for accuracy.