Ordinary Shapiro steps were observed in the I-V curves of biepitaxial Josephson junctions at V-n = nhf/2e when microwave radiation at f = 11 GHz was applied to the junction. However, pronounced current steps were observed at twice the period, V-n' = 2nhf/2e when the d.c. Josephson current was suppressed by high power microwave radiation. The extension of the voltage region, within which the double period steps were seen, increased with microwave power. Modified biepitaxial heterostructures of YBa2Cu3O7-delta, with (110)BaZrO3 as a seed layer and (001)CeO2 as an intermediate buffer layer were grown by laser ablation on (001)SrTiO3. The I-V characteristics for the biepitaxial YBa2Cu3O7-delta Josephson junctions agreed well with the RSJ model for T > 50 K but showed hysteresis at T < 30 K. No large excess current was observed. The critical current density, about 60 kA cm(-2) at 4 K, was an order of magnitude higher than for bicrystal junctions and prevalent biepitaxial junctions with a 45 degrees misorientation between the crystal planes on either side of the grain boundary. An irregular magnetic field dependence of the critical current, I-c, indicated an uneven current distribution within the junction. The IcRn products for the junctions were about 1.5 mV at 4.2 K and 20-60 mu V at 77 K. Pronounced current steps in the I-V dependencies due to a.c. Josephson current coupling to self-induced electromagnetic modes at the biepitaxial boundary were used to characterize the junctions.