Advice needed. Can you take your bike on a cruise ship?

Hello everyone. We are going away on a family holiday this summer with our friends - two families with young(ish) children. Our respective wives and children enjoy swimming and eating ice cream but my friend and I get bored with this after about 5 minutes! We are both avid cyclists (road and MTB) and usually manage to convince our families that a holiday with a company like Neilson is the best option (where they have bikes galore and a load of trails to explore). However, this year we are gonig to try cruising... which my mate and I are rather nervous about!!!! We are looking at travelling with Azamara cruise lines - some of the stops look truly amazing (Kotor in particular).  If we were able to take our road bikes on-board and stow them somewhere in their bike cases we could get some amazing rides during port stops. But so far nobody has been able to give us a definitive answer as to whether this is possible. Does anyone know of any cruise lines who actively allow this? Many thanks for any advice you might have! If we can make this work, we may have found a holiday that keeps everybody happy! Keep those cranks turning!