Should we send a new/misplaced package to our first time customer?

We are a small consulting business (myself and my girlfriend) but very reputable and established for quite sometime. We do a fair amount of mail order. We recently had one of our customers say they never received a package. We shipped by UPS ground to the address they specified. It was tracked as delivered and signed for. They say that person doesn't exist. They expect us to send out a new package to them. We did our part, they lost it.

This seems to happen fairly often, where someone will sign for it, then it gets misplaced. People almost always call back and say, our bad. It was misplaced.

What would you do? Spend the cost of the item plus a new s/h charge to replace this for them? or say sorry we did our part. We did fax confirmation of delivery BTW