Some avian vets can microchip cockatiels. Some won’t do it because they’re small, and the microchip is quite large, but it is possible. We had ours chipped. It works just like a dog or cat where if found, the vet can scan them to get the chip number & call the company who will in turn have your contact info.
Microchips are generally safer than a leg band because they can’t get caught on anything, but I do remember it took Cricket nearly a month to recover from his, as it goes into their breast muscle and it’s itchy while it’s healing. Once it healed though, he never seemed to be too bothered by it.