Man that is definitely up there in years but those cars are keepers. You should include a copy of your failed smog report with identifying info blocked off. Certain high readings like HC or NO can point to different parts failing. The trouble with those cars too is that they rely on an older OBD0 system which can miss worn parts malfunctioning. If the car is still running so-so and depending on where you live I might recommend just going for a crooked smog check. If the legit repair involves you replacing the catalytic converter then it may not be so worth the trouble.

If not already done you could try giving it a complete tuneup (plugs plus cap, rotor, and ignition wires) and make sure any available adjustments (ignition timing, etc.) are set to factory specifications if not computer-controlled. How old is the O2 sensor? Thermostat? (Is the engine reaching full operating temperature?) Is the EGR valve working? Vacuum lines and emission control gadgets intact?

As I recall Honda was still using a carburetor on some models in 1988. If you have that make sure it's properly adjusted. (Passing emissions tests with a carbureted 1980s vehicle can be real challenge. I used to go through that with AMC Eagles.)