The transport properties of the percolation channels of memristive structures based on YBa2Cu3O7−δ epitaxial films were studied. Molecular electronics and Andreev reflection spectroscopy were utilised, and the influence of the superconductive transition of electrodes on resistive switching effects in these structures was examined. Based on the analysis of the conductivity mechanisms in the obtained heterostructures, it is assumed that percolation channels form through a chain of domains disordered by oxygen about 10 nm in diameter, with a maximum Tc of 60 K. Zero-bias anomalies of the dynamic resistance of the studied structures display temperature dependence of the critical current of typical superconductor—normal—superconductor weak links within the framework of Kulik–Omel’yanchuk theory in the dirty limit. A simulation was used to determine the physical parameters of the studied heterostructures.