I was going to suggest slightly complicated way of determining the voltage drop of the LED by lighting it up in a circuit with just the LED, a battery and a resistor all in series and measuring the voltage of the battery, the resistance of the resistor and the current through the circuit. This way you can determine the voltage drop of the resistor by multiplying the resistance and current and subtract that from the battery's voltage and get the voltage of the LED. Or you can just switch the multimeter to measure voltage and measure the voltage across the LED when it is lit. That doesn't even require you to take the LED out of the circuit it is in.

The only problem you'll have if the voltage is too low is it won't be as bright. Of course, if I just replaced a random LED with a superbright with my luck the superbright would require much higher voltage and so when I put it in it would actually be dimmer than the LED I replaced.