as Darcy told you, do your homework before you go. Know your prices. The prices can be all over the place depending upon the diamonds cut, clarity, quality and weight.
Attend the port shopping lectures they are very helpful.Shop the recommended stores, that way you get a guarantee from the cruise line. Either St. Maarten or St. Thomas are great shopping ports. If you find something in town that you totally love and must have, buy it , don't wait and hope that you will find something better or cheaper at the next port. Check the ships sales also.