A method for producing a self-supporting ceramic composite structure, which includes a ceramic matrix embedding a filler, includes oxidizing a parent metal to form a polycrystalline material comprising the oxidation reaction product of the parent metal with an oxidant and, optionally, one or more metallic constituents, and the filler embedded by the matrix. The method includes heating a first source of molten parent metal and a reservoir source of molten parent metal and contacting the first source of molten parent metal with a permeable bedding of filler. The first source of molten parent metal is reacted with the oxidant to form the oxidation reaction product and is replenished from the reservoir as the reacting continues for a time sufficient to grow the oxidation reaction product to a desired extent and thereby embed at least a portion of the bedding of filler within the oxidation reaction product to form the ceramic composite structure. The bedding of filler may have any suitable shape, including that of a hollow body, the interior of which is contacted by the first source of molten parent metal to grow the oxidation reaction product through the shaped, hollow body of filler.