I have not been on the Liberty but I have been on it's twin sister the Freedom of the Seas and I can tell you that the ship does not rock. It's way to big to be affected by the regular motion of the ocean. 99% of the time you do not even know that you are even moving. In addition, if there is really bad weather, like a hurricane, the ship will steer away from it. June is the beginning of the hurricane season but thus far this year there has been no mention of any tropical storms and there are not usually Hurricanes in June. So you should have a smooth ride.