Yes there is a limit set by customs. Not sure but I think it is $800 per person. It is a different limit on booze.
It should belisted in your paper work you receive about 2 weeks prior to your cruise.
You have a form to fill out before you get off the ship where you have to list everything you bought and how much it cost. Save your receipts!!!
You do hand it to a customs agent as you are exiting the terminal baggage area. They do random bag searches.
after 13 cruises we have never been stopped or checked, just asked about what we bought a couple of times.
20 DCL cruises and counting!
1 Carnival Glory cruise
Waiitng for the new ships to arrive for more magical cruises!!