Presidium rhymes with:
chriptosporidium, cryptosporidium, idiom, iridium, nephridium, chriptosporidium, compendium, cryptosporidium, idiom, indium, iridium, medium, myocardium, nephridium, odiaum, palladium, plasmodium, podium, radium, rhodium, sodium, stadium, tedium, vanadium
Presidium sounds like:
persecution, pirestani, precaution, preston, pristine, progestin, projection, prosecution, prostitution