A tunneling microscope for future use in a variable temperature range from 2 to 300 K in magnetic fields up to 3 T is used to characterize the surface of epitaxial thin films of the HTSCs YBa2Cu3O7-delta and Bi2Sr2Ca1Cu2O8+delta, which are optimized with respect to superconducting parameters, at ambient conditions. The surfaces of the investigated YBa2Cu3O7-delta thin films are covered with screw dislocations of different shape and size, depending on the preparation process (pulsed-laser deposition (PLD), DC sputtering, chemical vapour deposition (CVD)). On "ideal" single crystals, up to 250 nm X 250 nm large, atomically flat areas separated by steps of one, or two unit cells of YBa2CU3O7-delta (c = 11.7 angstrom) can be discerned. Attempts are made to correlate the observed microstructures on the surfaces with deposition parameters. High-quality epitaxial Bi2Sr2Ca2Cu2O8+delta thin films show atomically flat terraces with steps which are multiples of half of the c-axis of the 2212 phase.