Upvote:2
Sleeping in Schiphol is allowed, but there is very little opportunity to do so on the Plaza side, but I've seen people put sleeping bags and mattresses down there, so there's always that.
There are more than enough benches beyond customs. If you can get to this side, you could also choose one of Schiphol's hotels: Hotel Mercure or Yotel. If your flights are on the same booking, this should not be a problem. If they are not, you'll have to see if you can check in at this point.
Of course you can always go to Amsterdam itself. Amsterdam Central Station is a 15 minute train ride, with at least 8 trains going per hour.
Upvote:3
You can wait in the Arrivals area after customs if you like, although obviously it won't be comfortable. You can also wait around in the Schegen departure lounge, if you are arriving on KLM, and then exit out to meet them when they arrive. The shops and restaurants will be open until a little after midnight. If you are using a low cost carrier I believe they use a different pier which may have reduced departure facilities. Also, if you have any check in baggage it may be removed if it is not claimed within a few hours.
Personally I would find a cheap hotel and meet them in the morning.