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The electric properties of interface-engineered junctions with YbBa2Cu3O7 as the counter-electrode were investigated. The junctions exhibited excellent Josephson characteristics with the critical current density (Jc) ranging from 102 A/cm2 to more than 106 A/cm2, and the normal resistance (Rn) ranging from 10-6 Ωcm2 to 10-9 Ωcm2. The Rn values varied approximately in accordance with Jc-p, where p was close to 0.25 for low-Jc junctions and increased gradually up to 0.75 for high-Jc junctions. The junctions with Rn exceeding 10-7 Ωcm2 exhibited dI/dV profiles peculiar to tunneling processes via localized states. The dI/dV profiles of the junctions with lower Rn were characterized by reproducible fine structures below 15 mV, probably due to multiple Andreev reflections. These results indicate that the crossover from the tunneling regime to metallic weak-links takes place in these junctions depending on the process conditions.