Shopping Around for Title Insurance

Has anyone ever shopped around for title insurance? My husband and I decided to proceed with refinancing both of our properties, but I hate the thought of paying for two more title insurance policies. I believe the title insurance on our rental home can be reissued, but I think we will need to purchase a new policy for our primary home. Our lender provided the name and quote of a title insurance company, but I’d like to shop around first to see it’s the best deal. Has anyone ever shopped around for title insurance? If so how did you go about finding and choosing the title insurance company?