Madrid rhymes with:
grid, rid, adid, amid, bid, cid, counterbid, cyd, did, forbid, grid, hid, id, ihde, kid, kidd, kidde, kyd, lid, majid, mid, quid, rebid, redid, rid, schmid, sid, skid, slid, smid, squid, stidd, syd, tidd, undid
Madrid sounds like:
mattered, matured, maturity, meandered, mentored, meteorite, metered, metrodade, mithridate, moderate, moderated, monitored, moothart, motherhood, mutert, muttered