When I used to live in Massachusetts, emissions testing was done annually with a tailpipe test (with the car warmed up and at idle). Newer cars were required to meet the limits in force when the car was built, but cars older than a certain age (10 years, if I remember correctly) were exempt. I think the logic to the exemption was that a lot of old cars were off the road by then, and those that were still left were driven by those not well off enough to be able to afford substantial repairs to bring a non-compliant car back into specs. Now I live in Vermont, and the only testing is done on OBD-II cars, and all they do is to hook up the diagnostic tester to check for codes. No tailpipe check is done.

Anywhere I'm aware where emissions tests have been implimented, there is never a requirement for cars to meet emissions criteria more strict than when the car was built. In the US, that means cars built before 1968 have essentially no restriction, and the limits only became difficult around 1974.