Wiktionary
vb. 1 (context transitive English) To fasten with a button or buttons. 2 (context intransitive English) To fasten all the buttons on a coat, or similar item of clothing, to keep warm.
WordNet
Usage examples of "button up".
At one point, a battalion of infantry did launch a deliberate attack, supported by mortars that forced the tank and Bradley crews to button up and reply with organized fire.
He took a microannealer and opened the button up and looked at its insides with a microviewer.
If Anakin were indeed safe, then he could button up the ship and wait this thing out.
I move toward him with the ax in one hand, and with my other I button up the raincoat.
Bock waited for the neighboring tanks to button up, then shot all three Russians with his silenced automatic.
When the pilot rolled out on his new heading, the OSO moved his cross hairs directly on the box, clicked the left button on his radar controller down twice, then clicked the button up.