as the others have said be informed before you go. Go to your local jewler, find something similar to what you are looking for and use that price as a guideline.
Attend the ships port shopping lectures, with a large ticket item such as diamonds i would stick with the major stores and the ones that the ship recommends. We have had very good luck with Royal Caribbean and Diamonds International. Less pressure sales in St.Maarten over St. Thomas. IF you find something that you love, buy it! don't wait and hope to find the same thing on another island for a better price, you will be dissapointed. Shop the sales at the ships jewerly store.