Composite electrochemical cells incorporating press-contact pellets of yttria-stabilized zirconia (YSZ), electronically blocking electrodes, and YBa2Cu3O7-x, (YBCO) were investigated by ac impedance spectroscopy. An additional element, not attributable to either of the individual components, was observed in the impedance spectrum of the composite cell. Although the capacitance associated with the additional element (similar to 10(-11) F) appeared to indicate a built, response, the capacitance was found to be invariant with dimensions of either the YBCO or YSZ components. A similar additional element was observed when YBCO was replaced by other electronically conducting materials, including gold foil. These results point clearly to an interfacial impedance whose characteristics are governed largely by the YSZ; the extremely low capacitance value arises from a very low effective contact area (10(-3)%) due to surface roughness. We found no features in the impedance spectrum which could be attributed to oxide ion conduction in YBCO. In the assignment of impedance spectra to the components of a heterogeneous system, it is demonstrated that the use of relaxation frequencies (f(rel) = [RC](-1)) and their temperature dependences provide a useful comparison, free from geometric factors, between samples with different origins or thermal histories.