I have two sinks separated in my master bath and both cold sides of two handle faucets are not working at all. It's not the airaters as both hots sides work. The water is turned on and one cold water line feeds both sinks, every other faucet works both cold and hot sides. Any ideas

I'm assuming that the angle stop's turned on. It sounds like some mineral buildup broke loose and is now clogging the cold water seats.
Try this,
Turn the water off at the angle stop and remove the cold water stems and washers. Check the washers for wear and the seats fro rough edges or nicks. Now place pans over the open valve bodies and turn the water back on to flush out the supplies. You should have a strong stream when you're doing this. If not click back and tell me about it. After flushing the lines reassemble and test, Better now? Good luck, Tom