Typically once your kids get married, and thus normally moved out of your household and into one with their spouse, they cannot stay on your (the parent's) car insurance policy. Your policy normally covers those in your household and perhaps a child that is away at college depending upon how far away the school is from your residence.
Usually when a child moves out of the house and/or moves out and gets married the parent's insurance company would not want to cover the child any longer since he or she dwells in a separate resident and not in the same household as the parents.
Each state and insurance company has their own rules and guidelines regarding auto insurance so you can check with your insurance company to see what they say about your specific situation and if your kids can remain on your policy after they are married. If they are still living with you and now married then you may be able to keep them on your policy since they are household members and need to add their spouses to the policy as well.
In general when your children get married and move out on their own with their spouses they will need to obtain a car insurance policy to cover their vehicles together in both their name and their spouse's name and be taken off of the parents' policies. If the cars the children have are in the parent's name then you may need to add the child's name to the title so they can register and insure the car in their own name now that they are married.
If your children have moved out of your household and need their own policies they can start shopping around for car insurance online for here with us.