Braking resistor calculations...

[Muzzer]

If this is a 12V motor, then the maximum voltage you'll get out of it will be.......12V or whatever voltage you were driving it with. This would allow you to calculate the peak dissipation you'd ever see, although this would rapidly fall off as the speed fell, so the nominal power rating could be a fraction of that, depending how often this would be happening. Bottom line is, does it even get warm in normal use?

You can work out the internal temperature rise if you dumped all the kinetic energy into the thermal mass of the resistor winding - this would be the very worst case condition and the skill is not to approach the melting point of the wire. But instead of doing fancy sums, it is simpler just to select the right kind of resistor. That would be a wirewound or foil resistor (they have a decent mass of metal in them), rather than a thin film resistor.

The motor will stop more quickly into a resistor than a short circuit. You'd want to make sure you didn't switch the short across the motor when the drive was working.