Will your insurance go up if you voluntarily give up your car?

If you give up your car, cancel your insurance, as you don't need insurance if you don't own a car. If you are talking about a voluntary repossession, the answer, is possibly, on another car. A repo is a repo, no matter if it is voluntary or not. Your credit will be damaged for 7 years, and this may effect you insurance rates. Don't do it or let it happen. Contact the lender and work something out if possible.