The law basically says that all cars 2-24 years old must be tested for emissions, and it defines a 24 year old car as a car with a model year that is equal to the current year minus 24. That means that in 2014, a 1990 model year Miata will be considered 24 years old and require an emissions test. In 2015, all 1990 Miatas become exempt.
With that said, a modern LS engine with a modern ECU should put out significantly cleaner emissions than a stock 1.6 Miata engine.