After defeating Unova's Elite Four, you will be sent to N's Castle, where you need to fight and catch Zekrom for the storyline.
Master Balls cannot be used to catch it, and its catch rate is improved here. In case you don't have any other possibility or run out trying to catch it, you need to finish the fight to be teleported outside of the castle to the Pokemon Center.
If you lose the battle or need to leave the castle, the way to go back in is by talking to the Team Plasma Grunt inside the Pokemon Center by the Elite Four's entrance.
After finishing that part of the storyline, you won't be allowed to keep Zekrom. It will stay in your house, inside your room. There is no way to claim it again.