*Insert standard "not a pilot" disclaimer here*
The only examples I know of were a result of pitot-static problems rather than the warning system itself. I think that the general thing to do would be to work out why you're getting an erroneous overspeed warning - set pitch/power, see which side (if either) has correct airspeed information, flick the selector over to the side which is correct and finally decide whether to continue or land immediately.