Compositions and methods employing supercritical fluids, e.g., supercritical carbon dioxide, for removal of unwanted material from microelectronic device structures and process equipment. One composition of such type, having utility for removing flux and solder perform surface films, includes supercritical fluid, e.g., supercritical CO.sub.2, and organic co-solvent, e.g., xylene. Another composition of such type having utility for removal of metals, metal oxides, metal-containing post-etch residues and CMP particles from semiconductor substrates includes supercritical fluid and at least one .beta.-diketone.