Along the lines of @TimWescott s comment, I presume you have a circuit which looks like
simulate this circuit – Schematic created using CircuitLab
where V1 is a current-limited variable power supply.
Rather than depend on the supply voltage meter, try the following. With the voltage set to five volts or more and the current limit set to zero, connect a DMM set to measure current as the power supply load. Increase the current limit setting until you have something like 200 mA being provided. Short circuit the output and disconnect the meter. Now connect the LED and release the short circuit. Use the DMM to measure the LED forward voltage. Good power supplies have fairly accurate output meters, but there is no guarantee that you have a good one.
Alternatively, if you don't want to depend on your current limit function, get a 100 ohm, 5 watt resistor. Spend a little extra and get a 1% unit. Set the current limit to something like 1 amp. Connect the LED like
simulate this circuit
Now set the supply voltage to something like 12 volts. You should be reading a load current of about 100 mA. Now measure the LED forward voltage.