Customers want to add to CC order after checkout

I use Authorize.net, and at least once a week a customer emails (before shipment) to add items to their order. I don't know where, or if, I can find their CC # to charge them for the added items. Up till now, I have just told them they need to go back to the website, order the item, and I send them a coupon, or process a refund for the additional shipping they pay through the website. It would seem a simpler thing to just be able to charge their CC for the item itself - without the requirement that they re-login, purchase, etc...

Any suggestions?

You're doing it the best way I can think of.

Thankfully for those of us who shop online, sellers who use a proper credit card merchant account (like authorize.net) can't just charge stuff to our credit cards on their own.

I'd be interested in knowing what you sell, since a customer who wants to add to an order is rare, in my experience.

We sell repair parts for vintage Italian espresso machines (one's who'se manufactures don't exist any more, hence, 'orphans'), and go-withs, like cups, and scales, tampers, etc...

So far people are pretty understanding about having to go to the site & place the order....