Any way for a servo or stepper to hold/lock position with power off?

I need to be able to rotate a servo or stepper to any of four positions (+/- 45 and 135 degrees) and then lock in that position with power disconnected. Is there some kind of servo or stepper that does this? Is there a way to apply an external brake or locking pin?

Ideally the motor would be about a 1 inch diameter, it wouldn't need huge torque in the turning operation, but would need to resist occasional bumps or impacts without moving. (Or failing that, a way to read the position at the next update if it is forced off the intended angle.)

If you drive it through a mechanism that has less than 50% efficiency then it will not be mechanically reversible, in other words you will not be able to move the input by pushing the output. A common way to achieve this is to use a worm drive, which typically have very low efficiency.

Thank you, Peter, that's a promising lead.

Or, if you can find one, an electromagnetic clutch/brake that is engaged on power-off.