Is there a grace period to pay my car insurance my payment is due on the 30th of each month?

This is dependent upon the state laws and regulation where you reside. Generally you will have a grace period of 10 days after the premium due date before the policy cancels. The only time this would not apply is at your renewal date. The renewal is a date that has no grace period. On the date the policy expires, it expires and is not active any longer, so you need to be careful with the renewal offer as you may or may not be able to renew after this date.