A few years ago this happened to a law firm I was working with.  Sadly, it was more time and cost-efficient to "eat the cost" and NO ONE is ever allowed to use UPS again - unless the client sends the UPS slip, requires it and takes full responsibility.  Delivers Horribly Late isn't even an option.

In hindsight, the funniest UPS incident before eMail, eDocuments, pdf attachments, etc.:  A package of M&A legal documents that MUST BE DELIVERED, signed and returned immediately - i.e., have the driver wait 5 minutes to accept the enclosed return envelope.  Sent on Tuesday afternoon for Wednesday morning delivery.  At 1 am Thursday morning a very tired and MAD CEO and a notary finally got the documents; I was really tired of sitting in the office making phone calls, too.  Wednesday beginning at 3 pm when documents were "still on their way," and calling every hour on the hour shortly after midnight  the dispatcher finally 'fessed up and stopped giving me the "documents are on the truck and on their way" line. The driver was brand new, new to the major city, and had gotten so lost he couldn't even tell anyone where he was (apparently also a "bad" neighborhood to be in at night).  A more experienced driver went out to find him and would deliver our package - time and date sensitive documents a day late.

Fine print: UPS, FedEx and DHL don't cover the much of anything if the package is lost or destroyed.  We find FedEx to be 99.9% reliable and, if there is a issue, has great customer service.  It is worth it to us to pay more than risk the "one" error.