While you never had a chance to properly battle against N before beating the game, you'll have a good opportunity to afterwards.
N's Castle can be found from one of the caves towards the backend of Victory Road after beating the game. Previously, there was a Zoroark blocking the path, but now the cavern entrance to the old castle is clear.
Down in N's Castle, he'll follow you around for awhile, but will then battle you when you reach the old throne room using only his legendary Pokemon. The one he uses depends on which version you're playing.
N uses Zekrom if you're playing Pokemon Black 2 or Reshiram if you're playing Pokemon White 2. He does NOT use both on his team.
After beating him, he'll give you either the Dark Stone (Black 2) or the Light Stone (White 2), which you can bring to Dragonspiral Tower to catch Zekrom or Reshiram.
Before you can have a rematch against N, you must first have captured both Kyurem and either Reshiram or Zekrom, you must have taken a ferris wheel ride with him in Nimbasa City (he appears there on Friday), and you must have also waited for the season to change since your first battle. He'll appear back in his castle, although will use a very powerful team against you depending on which season it is.
His lead Pokemon has an ability that sets up a constant weather condition (Politoed has Drizzle and Ninetales has Drought — their Hidden Abilities), while the rest of his team takes advantage of the weather change. Your best bet is to try shut off the weather conditions by bringing in one of your own, although keep in mind that several of his Pokemon have moves that will reinstate the weather condition.
You can battle N once per season.