This Honda idles normally most of the time. When it doesn't, it sputters then revs up then starts sputtering again. I have replaced the main fuel pump relay.

Assuming the ignition system (Ignition Control Module, coil, rotor, and cap) is in good shape, I would ensure all air is purged from the cooling system and I would clean the Idle Air Control Valve (IACV). I would also clean the throttle plate, throttle body, and upper and lower ports. FYI, I recommend replacing the Ignition Control Module and coil every 125,000 miles or 10 years, whichever comes first. Replace the rotor and cap every 60,000 miles. My gut is the ICM may be bad. Finally, change the fuel filter, if it has not been replaced in 60,000 miles.