Credit Card Registration Page
You can set up a Credit Card Registration Page using a Registration, Sales, and Cash Donation type page with only the option to save a credit card for use at the event enabled. All other options like tickets and donations are disabled.
Tips and Tricks
If you only want to share the page with certain people, make the page "hidden" by setting the Page Visibility to "Show page on website but don't show in navigation" so that it's only accessible via direct URL and create a friendly URL.
After a supporter registers a credit card it will appear in Import Online Purchases & Registrations where you can match it to an existing supporter record.
Add a link to a credit card registration page to your post-event receipts before contacting those with outstanding balances to encourage people to provide a card to pay an open invoice.