Anxiety and the meditative state are, to put it simply, impossible to experience at the same time. Who is it that is anxious, when that anxious person no longer exists?

In my experience meditation effectively reduces panic, but I'm still aware of panic. It's like holding a hot coal.

The hot coal is in your throat, not in your hand. Do you try to swallow it, or try to spit it up?

Swallow. "try to spit" sounds like trying escape, and I think it would intensify the anxiety. But spitting does involve letting go. Hmmm maybe I'll try it. Now what would make me anxious.

I second this. Mindfulness meditation is really easy to pick up and has worked a treat for me.