I once worked for a jewelry store that had to make a claim on UPS "losing" one of a group of four packages with some pretty expensive diamonds in each.
Normally, we used USPS insured/certified and never had any trouble. But in this case, the distributor needed his diamonds back really fast so we took a chance with UPS overnight.
We had carefully tracked and recorded exactly what went into each package, and insured each one for the exact amount of the value of the merchandise. The reason we had to split it into four packages was because of UPS's insurance limits at the time.
They actually paid up in a reasonable amount of time. Our distributor was happy, it was his biggest sale of the year. He encouraged us to use UPS more often.