Damage caused by drivers with no insurance — or not enough insurance — may be covered by collision insurance, depending on the specifics of the accident and the insurance company. Uninsured/underinsured motorist coverage is a great policy add-on if you're looking to avoid doubt about your coverage. Uninsured motorist coverage may help reduce your rate increase after a not-at-fault accident. While collision claims do raise insurance costs, uninsured motorist claims typically don't have as large an impact.