There are many resources online about packing your jewelry, wearing your jewelry on a plane, to going through TSA and what to do in case you travel with expensive jewelry.
The gist of it all is to 1) have a jewelry travel case, 2) have your jewelry in your on board luggage and NOT the checked luggage. 3) All jewelry, unless it is made of heavy metal will go through security easily. 4) the TSA will have your privately screened if you want them to and finally 5) if wearing or traveling with expensive jewelry, take pictures of your jewelry you are traveling with, and it is up to you to make sure that TSA finds your jewelry if stolen or lost. Also, do NOT flash your expensive pieces around and brag about their worth.
I hope this helps!
Flying With Jewelry FAQ - Get Your Questions Answered! – Roam Often