Just as a matter of clarification, we get asked is if the bikes can run without a battery. Technically the answer is "no" as the ignition coils are designed to be powered by a battery. My point here is that these Honda motorcycles do not have a magneto style ignition system commonly found on smaller dirt bikes and power equipment like lawnmowers or weed whackers (which will run without a battery). A healthy battery along with a charging system that is working well is what will keep your Honda CB350 / CB360 / CB450 or CB550 running happy. Often we find that an old or weak battery will cause all sorts of engine running issues with this era Honda motorcycles; this tends to tangent into chasing a ghost in other areas of the bike's sub systems attempting to pinpoint the issue. So be sure that your battery is reading a consistent 12V+ or better and is getting a full output from the charging system. Typical charging voltage for the Honda twins is 12.5 - 13.2 V+.
After playing with numerous batteries over the years we decided to only offer a top quality AGM battery, as a stock replacement on your Honda CB350 / CB360 / CB450 or CB550. A simple battery charger to keep it topped off as well as a new combo regulator rectifier are a worthwhile upgrade for the charging system of your motorcycle.