I shipped my ring off via UPS and yes, I took out the extra shipping insurance on the item which cost quite a bit extra. My ring also got lost for 3 days after I dropped it off and between the driver pickup, so that was scary but the ring made it its destination and I was refunded the shipping (excluding the insurance).
Do you have the item appraised? Do you have it insured with a company already (add to homeowners or a stand alone policy)? Both of these will help if the ring is lost.
Most vendors seem to use FedEx, and sometimes UPS. I'm pretty sure FedEx insures up to a much greater value than, for example, the post office. Generally I have used the vendor's FedEx account (they can email you the shipping label and bill you for the cost) and followed their detailed instructions about how to pack the item. Small box goes inside bigger box and maybe inside one more bigger box. Never had any problems. Overnight or second day delivery is also recommended, so there is little doubt about the item having been received and exactly when it is expected.