A method of making self-supporting ceramic composite structures having filler embedded therein includes infiltrating a permeable mass of filler with polycrystalline material comprising an oxidation reaction product obtained by oxidation of a parent metal such as aluminum. The self-supporting ceramic composite structure optionally contains therein non-oxidized constituents of the parent metal. The structure is formed by placing a parent metal adjacent to a permeable filler and heating the assembly to melt the parent metal and provide a molten body of parent metal which is contacted with a suitable oxidant. Within a certain temperature region and optionally, aided by one or more dopants in or on the parent metal, molten parent metal will migrate through previously formed oxidation reaction product into contact with the oxidant, causing the oxidation reaction product to grow so as to embed the adjacent filler and provide the composite structure. The parent metal may be provided as a body of metal placed in contact with an exterior surface of the permeable mass. Alternatively, the parent metal may be placed adjacent to the filler material by admixing a plurality of discrete bodies of parent metal (e.g., particulate metal) into the permeable mass. In this embodiment, the growth of oxidation reaction product still embeds the adjacent filler material without substantial change in the size or shape of the permeable mass, but does not result in the creation of voids at the former locations of the bodies of parent metal.