Get your no claim bonus : If you are selling your existing car and buying a new one , remember you are entitled to transfer your no claim discount from the old car to the new car. For example if you owned a Maruti 800 for 6 years and have never filed a claim then you are entitled to 50% no claim discount. If you are now buying a BMW you can transfer your no claim discount of 50% which will apply to the much larger premium payable on an expensive car such as BMW.
Compare car insurance sum assured before you compare premiums : Just like a life insurance policy there is a sum insured in a car insurance policy also. Only it is called Insured Declared Value or IDV for short. So if somebody gives you a cheaper quote for the same car check out the IDV. It should be the same for the two quotes to be comparable.
Keep a copy of all documents submitted to the insurance company for your future reference.
Any promise made by the agent or even an official of the insurance company has no value unless it is in writing or at least on email.
So if you are basing your decision on any such promise make sure you get it in record in some form.