I've had lost bags several times-- usually they have the bag a couple days later, as +Sandy Gennrich
said; sometimes they make you come get it, sometimes they deliver it to you. If you had lost it at your travel destination, they would cover a certain amount for you to buy clothing; since they lost it on your trip home, and it doesn't turn up, they will reimburse you for some items lost. You may need to provide photos or receipts of the items, and the amount they cover varies.
The credit card would come into play if yours offers coverage on items you purchased with the card being stolen or lost through no fault of your own.