The best way is to have temperature monitors or thermocouplings to monitor the exhaust temperatures of the combustor.
When monitors are installed properly and the combustor has had ample time to reach light-off , the exhaust temperatures will rise immediately when the bypass damper is closed. This will indicate the catalyst is operating. Exhaust temperatures are important to monitor. As I mentioned in the last posting, temperatures above 1800° F. (1000° C.) will damage the combustor. Temperatures between 1400 and 1600° F. (760-870° C.) are common, but operating temperatures between 1200 and 1400° F. (650-760° C.) are recommended. Most of this heat is transmitted to surrounding stove parts via thermal radiation.
If you don't have monitors, just go outside and see what is coming out of the chimney. If the bypass damper is closed there should be no dark lingering smoke coming out of the chimney. This will tell you the catalytic combustor is working fine.