Yes! You can allow your customers to cancel their own reservations. To enable this feature, navigate to Setup - Business Information - Changes & Cancellations.
You can set a cancellations penalty here (optional) and allow your customers to cancel:
Next, you'll want to edit your confirmation email template (How to edit Email Templates) to add the link to MyReservations which will enable your customers to access their reservation.
MyReservations link: https://www.webreserv.com/myreservations.do
The MyReservations link gives your customers also have the ability to view their balances, make additional payments of their reservations, and cancel their reservation.
Note: Customers are not able to make date or product changes to a reservation using this link. They must call you to make changes.
In order to access the reservations, they will need the Reservation Code, Last name, and Email address
After access, the customer will see the information on cancelling the booking, and the link to cancel:
Once the reservation is cancelled, the information will show to the customer the status, and a cancellation email will be sent to the customer (and the business).