Be aware that insurance quotes usually require pulling your credit report to make sure you are a 'good risk'. Several pulls (I was told once 5) in a year can reduce your credit score. Since your credit will also be pulled for a quote for buying a car, entering into a contract for services such as a cell phone, pre-qualifying to purchase a home, etc. etc. you my want to restrict your 'pulls' to things of personal value rather than shops. A lower credit score generally results in higher interest rates or denial of credit. If/when I do this kind of thing as a shop I dance around actually giving my social security number by asking them to quote me based on my estimate of what my credit score is and IF I decide to go with their product I will allow them to verify the score I gave them is about right. Sometimes it works, sometimes it doesn't. If it doesn't and is a shop, I will walk away from it.
I do have a Discover credit card which posts my credit score on every statement, so I do know what it is and if/when I next go car shopping, I will take along my most recent Discover statement to show my recent score for a quote without pulling my credit.