I know I keep posting to old threads, but my comments are still relevant here.
I've had extremely bad hand tremors at times, due to stress and anxiety I think. I actually got myself Baker Acted (a Florida thing, similar to a 5150 in California) because of my tremors, and coincidentally wound up at a hospital that my outpatient psychiatrist just happened to work at. That hospital also just happened to be able to work with tremors, although it was a bit of an odd experience. I have both essential tremor AND drug induced tremors.
I take Artane for my tremors. The usual medication for tremors is propranolol, but in my case, my tremors were so extremely severe that the required dose of Propranolol would have been lethal. Propranolol lowers blood pressure because it is a beta blocker. Artane was the next drug of choice, and is actually used for treating Parkinson's disease. It helps a bit, but it also dulls my brain a bit because it can (in rare cases) cause issues with memory and clarity of thought.
My therapist actually wants to start tracking my caffeine and sugar intake to see if there's a relationship to my tremors (or anything else for that matter).