There are only 11 (eight?) counties in Ohio that have emissions testing.
In those counties, anything over 25 years old is exempt. Anything under 25 years old must be tested upon first registration, and every other year thereafter depending on model year. (So if you already own the car, the cutoff is effectively 24 years)
The pre-OBD-II test is a simple 25mph roller test, unless the vehicle is AWD, in which case it's a 2000rpm fast idle test, since the test stations do not have AWD dynos.
You'll like how cheap it is to register cars here. Two cars runs me roughly $165 annually - $55-58 per car, plus one has a personalized plate which is an additional $50/year. Fees are based on what county you live in, there's a state fee and an additional county fee. I live in one of the more expensive counties, some counties are as low as $40 per car.