Once you check various travel websites, go to the actual airline website. Some airline websites guarantee their lowest fares on the web, and by going through the airline website, you don't have to pay a booking fee on top of the airfare.
Example, you see on Travelocity that United has a direct flight. Before you book anything, check United's website to see if the fare is any cheaper for the flights that you want.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)