Compare coverage, not just price
Before you switch, line up the new quote against your current coverage limits, deductibles, and add-ons — not just the headline price. A cheaper policy with lower limits or missing coverages isn't an apples-to-apples comparison. An independent agent can put several carriers side by side for you.
Line up the effective dates
Set your new policy to start on or before your old one ends, then cancel the old policy for that same date. Never cancel the old policy first and shop later — even a short lapse can raise future rates and, in many states, affect your registration.
Confirm, then cancel
Get written confirmation that the new policy is active before you cancel the old one. Ask your old insurer for any refund of unused premium, and update anyone who needs proof of insurance, like a lienholder.