As suggested by Penny, if you haven't already, call Princess and tell them of the lost item. Besides that, there's not really much you can do I don't think. Hopefully someone will do the right thing if they find it. If they do, then if they don't come to the forum and see the thread, they have to somehow "track you down" for lack of a better term.
There are people out there that do things. Example, my sister's friend left her camera in a New York City taxi. The person that got in the cab found it, started looking through the pictures to see if there was any way to identify the owner, found one of her and her fiance at the time (now married) at the Rutgers Half Marathon, contacted the Rutgers Half marathon and gave the person the marathon number of her fiance (he was wearing his Marathon Number in the photo), and the Rutgers Half Marathon contacted him stating someone found something that belongs to him, and got it back.
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)