They had smog equipment in '68?
That was the first year nationally for emission controls, which in '68 amounted to a PCV valve and maybe an air pump, depending. California started around '65 or '66 I think.
Both my vehicles are registered to my company. Emission testing is required in my county but after I opened an office in the next county I transferred the registrations up there where no testing is required. It isn't a matter of not passing ('04 Focus, '05 Sport Trac), just that I don't want to pay for it if I don't have to. As we know, air stops at the state and county borders.

If you want to register it as a classic or antique to avoid emissions tests, go ahead, but again depending on the state you may be limited to how many miles you can drive it annually.
Bud of mine, Ranger driver, has a fleet of classic Fords, they all have current plates, inspections, and emissions
because he and his mom drive them all the time except for a few months in the winter. (64 1/2 Mustang ragtop, 65 Mustang, 65 Lincoln 4-door ragtop, 76 Lincoln, 59 T-Bird, 77 LTD wagon)