Never pack your jewelry inside any luggage you plan to check. If your luggage gets mishandled or lost, your jewelry won't suffer the same fate.
Wear any jewelry that reasonably suits your traveling attire, taking care to not draw unwanted attention with layers of fine jewelry.
Any valuables that cannot be kept on your person should be stored in a carry-on bag. Ensure you choose an appropriately-sized carry-on bag to avoid plane-side check.
Ask the TSA officer to screen you and your valuables in private to maintain your security. Or, at the very least, hold onto your carry-on until just before you step through the body scanner, and collect it immediately on the other side.
Don't forget that, for international flights, you must report to Customs the transport of goods valued at $10,000 USD or more.