In some cases the premium can be substantial. In today's homeowners insurance climate, having two or more claims in three years can get you canceled. Their only recourse is to cancel your policy. By the same token, many companies offer a claim free discount. The time to shop for a better rate is not after you have had a claim.
Most insurance companies offer a credit to homes that have been completely renovated.
Complete means just that, interior walls, wiring, plumbing if other than copper or PVC, and new roof. If no one in your house hold smokes, inquire as to the availability of a non-smoking household credit. Frame vs. Brick Check your policy to see if your home's construction class is correct. If you believe your home is insured for too much, supply your agent or broker with a copy of your survey or building plans and ask that your home be re-estimated. Be prepared for the possibility that your home is not currently being insured for enough.