What can you do if you had an accident and a ticket was given but later cancelled and there is no violation on record but the insurance company is still surcharging for the accident?

If the insurance company had to pay anything for damamges, then they will raise your rates for it. An accident will be on your record whether At Fault or not and whether or not you got a ticket. Changing insurance companies may not save you much money. If you can get documentation proving the ticket was voided and your driving record is clear, forward it to your insurance company. If they refude to take it into consideration, file a compaint with a supervisor or a general director of the company. If that fails, you might want to think about shopping around.