Best Way to Ship & Insure Small, High Value items?

This is not a post about how best to pack & ship big, heavy amps & speakers & such (lot of great posts on A'gon on that subject). Rather, my question is which shipper is most reliable, & likely to pay an insurance claim, on a high value item, say.......$2,000 to $5,000 (or more). i.e.; how best to ship a relatively small but valuable item that can easily be shipped by air, & the weight & shipping cost is not an issue, & you're not as much worried about shipping damage as it possibly getting lost? I'm guessing, insured USPS priority or express mail? Thanks in advance for any feedback!