As pointed out, there are no irons allowed because of a fire hazard. However, a trick I learned from my dad was if you hang stuff up in the bathroom, the steam will take most of the wrinkles out as people shower. Or you can have it pressed by the laundry service onboard.
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)