Planarized layers of YBa2Cu3O7 (YBCO) were made by etching trenches in SrTiO3 (STO) substrates, laser depositing a YBCO film and mechanically polishing the film down to the substrate surface. These structures exhibited critical temperatures (Tc) of 88 K and a critical-current density (Jc) of 106 A/cm2 at 77 K. The planarized surface was smooth, with a maximum height difference between the YBCO and STO of 20 nm. The surfaces were used as templates for epitaxial growth of multilayer insulators of STO and PrBa2Cu3O7 (PBCO) and top YBCO layers. Complete crossovers, free of superconducting shorts, with Tc of 86 K and critical current density (Jc) of 2×105 A/cm2 were made.