Typically, once your adult child gets married and moves out of your home, he or she 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.
If your adult child is still living with you but is married, then you may be able to keep him or her on your policy, as your insurer would consider your child as a household member.
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.