Personally I would send them a feedback sheet with their invoice and include a comments section. I would probably use wording similar to the following:
“Thank you for using __________ for your event! We are always trying to improve our client’s experience and we would appreciate 5 minutes of your time to tell us what you think about your experience.
We respect our clients privacy and will keep the contents of this form confidential and anonymous unless you indicate in the box below that we may use your comments as a testimonial.
Thank you for your time and for using __________, we look forward to serving you again.”