Missileman, thanks for replying. The service adviser at the dealership said they checked for error codes, and there were none. The owner/mechanic at the foreign car repair shop I went to explained to me that inline 4 cylinder engines are inherently imbalanced, and that the problem gets worse as the engine size increases. (I think the car has a "balance shaft", but I'm not sure. I searched for it at an online parts web site, but I was unable to find a part by that name.) Regardless, I know my car did not used to vibrate like it does now.
In an online forum about "8th generation" Civics, other owners have complained about vibration at idling. No one seems to have found a resolution, though. Someone suggested using high octane gas instead of regular. I tried that, but the higher octane did not make any difference.
I remembered an incident that might be relevant: My car has an automatic transmission. One time a long time ago - before this vibration problem started - I was in Neutral and rolling forward very slowly (I think I was in a parking lot) when I accidentally shifted the car into Reverse instead of Drive. The car jolted backwards, obviously. I did not notice any problems immediately afterward, but I wonder if I damaged something in the engine or transmission, or maybe moved something out of alignment. I don't recall how long after this incident the vibration started.