It's important to ask about details such as the amount of liability protection, bodily injury protection and the kind of coverage provided if you're hit by an uninsured or underinsured motorist, notes Deeia Beck, the state insurance consumer advocate in Texas. If you'd rather have someone do the research for you, independent insurance agents are an option. Contact your current carrier. Your insurance company may be willing to fight hard to keep your business. It's amazing how quickly some insurers offer competitive discounts if you hint strongly at leaving, Beck says. Many companies will try to match or beat a rival's quote. Also, see if you're missing out on discounts with your current carrier.
Source: http://www.foxbusiness.com/personal-finance/2014/02/05/7-smart-steps-to-switching-your-car-insurance/