Experiments are reported on two techniques for melt-texture processing Ba2YCu3O6.5 by directional solidification from a semisolid melt containing particles of BaY2CuO5 and a copper-rich liquid. One of these employs an electric resistance furnace with ambient or oxygen enriched atmosphere; the other is a laser-heated furnace operating at 1.3 atm oxygen. Solidification interface morphologies and other structural features were examined in quenched specimens. Depending on growth rate and temperature gradient, three different types of growth morphologies of the growing 123 phase were observed: "faceted plane front," "cellular dendritic" or "equiaxed blocky." The interface temperature decreased markedly with increasing growth rate for the faceted plane front specimens. In the remaining specimens, solidification took place over a range of temperatures. The temperature of the "root" of the solidification front dropped, but temperature of the solidification front "tip" did not, A solidification model is developed and employed to interpret experimental observations. The model assumes limited diffusion of solute in the liquid during the growth of the superconducting phase. The model shows, in agreement with experiment, that growth rate of the low temperature solid phase has a strong effect on ability to obtain the desirable faceted plane front, and that thermal gradient has only a small effect. Interparticle spacing of the high temperature phase, BaY2CuO5, is also predicted to have a strong effect.