They can handle some huge waves without a problem. In fact on the Dream we were in what was easily 15 ft waves and I didn't know it until I looked out of the cabin window (Riviera ocean view) and saw water hitting the window. She was riding through them without any issue.
I would think wind is a bigger issue with profile these ships have. As long as he captain can keep the bow into the wind it wouldn't be an issue.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007