WordNet (r) 3.0 (2006):

button up
    v 1: refuse to talk or stop talking; fall silent; "The children
         shut up when their father approached" [syn: close up,
         clam up, dummy up, shut up, belt up, button up,
         be quiet, keep mum] [ant: open up]

Moby Thesaurus II by Grady Ward, 1.0:

68 Moby Thesaurus words for "button up":
   bang, bar, barricade, batten, batten down, bolt, button, cap,
   carry to completion, choke, choke off, clam up, clap, clean up,
   climax, close, close out, close up, complete, conclude, constrict,
   contain, contract, cover, crown, culminate, dummy up, end, fasten,
   finalize, finish, finish off, finish up, fold, fold up, get done,
   get it over, get through, get through with, key, latch, lock,
   lock out, lock up, mop up, occlude, padlock, perfect, plumb,
   round out, seal, seal off, seal up, secure, shut, shut the door,
   shut up, slam, snap, squeeze shut, strangle, terminate, top off,
   top out, wind up, wrap up, zip up, zipper