I usually recommend you purchase musical instrument insurance from
Heritage or similar. Make sure the insurance covers your instrument when it's being shipping on a common carrier. Often the price for annual coverage is comparable to one or two shipment's worth of declared value on UPS/FedEx, and some policies are transferable.
You can use the UPS declared value, but it's not insurance. You have to prove carrier liability to get paid. If damaged is concealed, you don't get anything.
Do not use FedEx declared value even if you use them for shipping. You need your own insurance for them. From their
Service Guide:
"F. Shipments (packages or freight) containing all or part of the following items are limited to a maximum declared value of US$1,000...12. Guitars and other musical instruments that are more than 20 years old, and customized or personalized musical instruments"
The same limits are on all levels of service from them, ground to overnight.