A process for producing refractory ceramics (K) for use as heat shield in the hot gas path of gas turbine plants: introducing a casting composition into a component casing mold for the refractory ceramic (K), closing the casting mold so that the casting composition is under a defined static pressure after closure; orienting vibration of the casting mold in the direction (V) of a normal (N) to a surface of the refractory ceramic (K) to be produced, and subsequently removing the casting from the mold and firing the cast component.