Bill after being told test would be no cost

I had a test done at the ENT doctor that is done fairly often. But it is expensive so the office always confirms the cost with the patient's insurance before scheduling. My insurance told the office this test would have zero cost. But after they submitted the insurance claim, I was left with a large bill. The office billing department has record of my insurance telling them this, which was then relayed to me. She spoke with a supervisor at the insurance company and has asked them to honor what they said. I am still waiting to hear back. Is there anything else that can be done if my insurance comes back and says I have to pay? I only went ahead with the test because it was free. It's something the doctor recommended but it wasn't absolutely necessary or an emergency situation.