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Low-temperature electrochemical measurements were carried out on interfaces between different polycrystalline high-Tc superconductors (YBa2Cu3O7-δ with 0 ⩽ δ ⩽ 0.5, YBa2Cu3(1-x)Zn3xO7-δ with 0 ⩽ x ⩽ 0.06, Tl2Ba2CaCu2O8, Tl2Ba2Ca2Cu3O10) and Ag β′′-alumina as a solid electrolyte. By using a special transient routine, cell currents were measured vs. time at a constant potential. From the d.c. limits of the transients, a significant increase of the current is observed around Tc which cannot be explained by a specific property of the solid electrolyte. This effect must be correlated to Cooper pairs changing the electrochemical double-layer structure and possibly penetrating the energy barrier at the interface HTSC/solid electrolyte. The results are interpreted as an enhancement of the electrode kinetics or a proximity effect.