A protective structure includes a substrate made of a nickel-base superalloy component of a gas turbine engine, and a ceramic thermal barrier coating overlying and bonded to the substrate. The ceramic coating is an open-cell solid foam of aluminum oxide ceramic cell walls having a porous interconnected intracellular volume therebetween. The ceramic coating is prepared by depositing a precursor material onto the surface of the substrate. The precursor material includes a sacrificial ceramic, typically silicon dioxide, and a reactive metal, typically aluminum, which is reactive with the sacrificial ceramic to form an open-celled ceramic foam. The sacrificial ceramic and the reactive metal are reacted together to form ceramic cell walls of an oxidized ceramic of the reactive metal, preferably aluminum oxide, and an interconnected intracellular volume therebetween filled with an intracellular metal. The intracellular metal is thereafter removed to leave a porous intracellular volume.