Sounds normal. Best way is with an adjustable bench supply and a suitable dropping resistor, maybe 10K. Ramp up the supply while monitoring the voltage across the diode. It should keep rising until you reach its breakdown voltage, then stay there as input voltage is increased.
Keep in mind if the diode is backwards, it will function as an ordinary diode with a 0.5~0.7V forward drop. You can verify this with your DMM on diode check.
+-RH