[UPDATE: The problem returned fairly quickly. It turned out that I have a head gasket leak between cylinders 2 and 3 which is also causing coolant to spill into cylinder 3. Compression gauges are cheap, so do a compression test; unplug the two connectors that go to the distributor to disable fuel and ignition for the test. My numbers were 160-120-25-150, and when I put oil in 3 and re-tested, I saw a puff of white smoke begin coming from the plug tube for 2. Clearly a bad head gasket. Fortunately, if I do it myself, it's about $300 in parts and machine shop work.]
I own a 1997 Honda Prelude. It had a random misfire problem, and to help fellow owners out, I wanted to quickly document what I did to fix the problem. My car needed lots of maintenance, but yours might only need some of these things. For reference, my problems began around 224,000 miles on the odometer.
First thing to try is reseating all the electrical connectors that involve your ignition system. My root misfire cause was a bad connection being made in the two connectors that go to the distributor pickup coil. Simply disconnect and reconnect the connectors and see what changes.
Next, make sure that you have good spark plugs and spark plug ignition wires, as well as a new distributor cap and rotor button. I always use NGK Iridium IX plugs because they last a long time, perform very well, and are not very expensive. The distributor cap has only three screws and the rotor button has one in the shaft, so both are simple to replace and quite cheap. This should be done as part of any tune-up anyway, but if you neglect to take care of all four of these parts, they can make life miserable for you.
If the electrical connectors and tune-up items are okay and you still get misfires, see if there is an oil leak in any of the spark plug tubes. You should notice oil leaking onto spark plugs if you try to take the plugs out, and any oil is an indication that it’s time to replace your valve cover gasket. The part is around $55 but it’s rare that you’ll need to replace it, so even though it’s annoying to get that cover off and do the work, you should knock it out anyway. I was an idiot and seriously over-tightened the nuts, which caused my gasket to compress and leak, so I had to replace mine twice. Valve cover gasket nuts on a Honda Prelude should be snug, and I don’t mean hard snug! As long as the rubber washers fill the holes they came from completely, and it’s gently snugged down, it should be fine. Don’t blow up a $55 gasket like genius boy me managed to do.
The last things to try if you still have problems is cleaning out the EGR ports and valve. It’s very annoying, but there are excellent guides out there that show the procedure in good detail. This will definitely help a funky idle and boost fuel efficiency, and if you’re past 200K miles, you probably need to do it anyway. The port plugs are sold by Honda, and are the same as the ones used for many Accord models.
I am not a professional mechanic. Please don’t ask me questions about how to fix your car. I am only posting this to help others because I struggled with this for many months, and the root cause ended up being a bad electrical connection that took 20 seconds to fix. If this helps you, please comment on it and/or link to it. Happy wrench turning!