Registered mail through the US post office is your best bet. You can insure any shipment for up to $50,000.
It’s cheaper than buying insurance from FedEx or UPS. And it’s very safe—your box will be locked up during the shipment process.
However it can be very slow. It could take anywhere from 7 to 18 days to be delivered from my experience.
You also have to seal every edge with brown shipping tape. You can find the tape on Amazon. It’s the type you have to wet down with water to stick.
I’ve shipped almost 100 packages using registered mail and every one was delivered.