If my multimeter consistently reads 19.9 to 20 volts ac when testing outbound current on a 16V doorbell transformer, is that too much voltage? The reading at the switch-button (with switch removed) is the same. The wires at the switch-button had been shorted together when we weren't home, and we returned to an electrical odor originating we think in the area where chime is located. I am trying to determine where the damage is in the circuit. If 20 volts is within the norm on the transformer then probably my chime is broken. If 20 volts is too much, then my transformer probably needs replacing.
Replace the chime, the coil is toast from the shorted wires when you weren’t home.
Open circuit voltage with the circuit at rest being 19-20 is nothing to worry about. (a doorbell is a momentary load device, the circuit is at rest 99.99% of the time. I avoided other terms like "open" and "closed" to describe the circut but based on your comment still confused.)