Due to unforeseen circumstances, you’ve had to cancel an event. You’re not sure if you’re going to be able to reschedule, and your organization has chosen to not issue refunds. If your registrants have paid and you wish to give them a credit toward a future event or invoice, you can issue them a credit memo. You can do this either from a contact record via the billing tab, or through the Billing module's Credit Memos tab.

Credit memos can be applied to any open invoice; it is up to your organization to decide if you wish to restrict their use in any way.

More details on issuing credit memos can be found here.