Here in MA, you can get "Antique plates". To get those, the car has to be 25 years old or older, and there are restrictions on when you can use the vehicle, since the cost of registration is about half of what a normal set of plates cost. You can also get "Year of Manufacture" plates which are cool. For years in MA into the 1970's, the plates have the year they were issued stamped into the plates. If you find a pair of them, and that plate number is unused, you can register your car as an antique with them!
Registering a car as an antique has zero effect on getting a state inspection, though. Here in MA, there's a rolling 15-year emissions exemption, so they have to pass a safety inspection only. They mainly look at if it has working lights, a horn, minimal body rust, no structural rust, and a front end that isn't falling apart. They do it all on camera now, so there's no fudging it like people would do on really questionable stuff in the old days. That's probably a good thing.