1. Put someone out 给某人添麻烦
Please don't go to too much trouble. I've put you out more than enough.
别费心了,我已经够给您添麻烦了。
2. Put someone up 留宿某人
I can put you up till my wife's back from her mother's.
你可以在我这里住,直到我老婆从娘家回来。