Usually the court will require you to show proof of insurance for the car you were driving, not car insurance for your own vehicle.
While it is good that you have your own car insurance policy, this auto insurance coverage would only extend as secondary coverage to someone else's car you are driving. Any vehicle you drive needs to have primary insurance placed on it by the car owner, and that is what courts usually want to see.
When you are ticketed for no proof of insurance and there is valid insurance on the vehicle, to get the ticket dismissed you should contact the court to see what documentation they require because it varies from one court to another, even in the same state.
Typically, you can get your ticket dismissed, or reduced to only court costs, by providing proof that the vehicle was in compliance with the state's financial responsibility requirements at the time the citation was issued.
This means bringing documentation from the car owner's insurance company verifying the car had valid insurance at the time of the ticket. The insurance on your own car isn't really relevant to the court because insurance follows a car first and driver second.
When driving someone else's car, it's not only important that the car is insured properly but also that you know where the valid proof of insurance is kept, so you can show it to an officer of law upon demand.
If you unknowingly drove a car that was uninsured, then you'll need to check with the court that was listed on the ticket to see what your options are. Some states allow you to get the charge moved from you, the driver, to the car owner, since that is who the state mandates carry the auto insurance coverage on the vehicle.
In some states, both the driver and car owner can be cited for no proof of insurance by law enforcement. In this type of case, you'd be out of luck, usually, getting the ticket dismissed.