You should have your new policy ready to go first, as you want to avoid a lapse in coverage. Once you have the new policy start date, give your car or homeowners insurance company notice of your cancellation. You can set the start date of your new policy for the day your old policy ends. By doing so, you'll ensure that your former company will stop billing you by the time your new policy is in effect. You'll also prevent coverage gaps between the canceled and new policies.