A life time ago I managed a club in the Hamptons. It was frequented by a number of swells, privileged spoiled brats really. I had a problem with bounced checks, so I made blown up copies and posted them in the entrance way. It was amazing how quickly people made good on those checks.
I ran a very high profile restaurant in NYC, four stars from the NY Times also written up in the Times as the best service in the US. It was frequented by celebrities, masters of the universe, politicians and even royalty. If someone was a notorious bad tipper and it didn't matter who they were, we did not accept their reservation. You have an obligation to your staff. They need to know you have their back and are not going to let customers abuse them.