Last year California, Arizona, Idaho, Louisiana and Minnesota among others put in regulations to allow you to display your proof of auto insurance on your smart phone, tablet or other electronic device. Other states are starting to follow this trend.
What shoud you do? Check with your carrier to see if they have an app or better still check with your decvices store (Apple Store, Google Play Store, etc.) and search for your carriers app. You will have to have your policy information to set up the app and you may have to set up an online access with the carrier.
Remember that you must have proof of insurance whenever requested by law enforcement. I would still keep a copy of the id card in your glove box or wallet just in case you loose your device.
You can read more here.