There are many private health insurance companies and the quality varies. Some are provided by a single hospital - British Hospital, for example. Though they may be good in many instances, the problem is that you are limited to one institution and its staff. I am insured by OMINT. It is a bit expensive, by local standards, but the service has been excellent and I have a long list of doctors to choose from and can go to all of the leading private hospitals. Other insurers you might consider are MEDICUS and Swiss Medical. There are others. Check around. In the worst case, you go to a public hospital.