I was told to attach wires to the LED being tested in a "K" shaped fashion (thanks evan9162). What I mean by that is have a pair of power leads go to the emitter from the power supply (and soldered to the emitter or star), then have a second pair of wires attached as closely to the emitter or star as possible to reduce voltage drop (caused by current being passed through a wire -ohms law). Hook your multimeter to the pair of wires that are not attached to the power supply. Just like the K-shape, the node is as close to your emitter as possible.
With this set up, you will have a very accurate forward voltage reading that will not get skewed from having a voltage drop in the wires carrying current. If you have a power supply that can go in to a true constant current mode (CC), then you can use thin wires between the power supply and the LED, since voltage drop in the long, thin wires will never be measures by the multimeter if you are using the above configuration. In CC mode, the power supply will output the same current, regardless of voltage. Therefore, it does not care about the 0.5V (for example) voltage drop in the series attached power leads. The multimeter will never measure this voltage drop.
Do not be too critical of your setup if your LED emitter has a Vf of 3.7V at 350mA. Oh, and datasheets show a very approximate value of Vf, so trust your actual measurements of your particular emitter, and sort of ignore the datasheets. Every LED emitter is different in its own way! I have some LEDs around that has a nice, low Vf of 3.07V at 350mA, lots of LEDs that show 3.2V to 3.3V at 350mA, and a couple of oddballs that show 3.5V to 3.7V at 350mA! For most of my LEDs, it is expected because I know their forward voltage bin code. Only older LEDs and Crees that I have do not have such bin, so I have to go by my measurements. It is too bad that the first LED that you tested for Vf has such a high forward voltage! It is also too bad that Cree does not bin their LEDs for Vf like Seoul and Lumileds. That is the nature of the Cree/DX lottery
. If you can, try another emitter.
+1 on what TigerhawkT3 said. Your LED still has a good use: for DD flashlight configurations with li-ion cells. Your Q2's forward voltage range nearly matches that of the voltage range of a li-ion cell throughout its life!
Finally, do not fear that your LED will fail at 1.1A. As long as you have it attached to a large heatsink of some sort (maybe with a thin layer of thermal paste), then you will be fine. The XR-E emitters, like the Luxeon K2, can handle currents up to 2A as long as it does not get dangerously hot. 1.5A is the maximum recommended current for extended periods of time. The company gives a max of 1A, which is a good maximum for flashlights with some decent heatsinking. 700mA is a good current for decent efficiency and great brightness. At this current, your flashlight will start to get pretty warm. 350mA is the rated current for when the color and forward voltage (as well as luminous flux) is exactly what the bin codes state. Oh, and the maximum efficiency of most power LEDs sit at the 50mA to 350mA range (usually where the efficiency curve is relatively flat and at its peak). I hope that is helpful. The above currents are approximate, depending on the Vf of your LED. A LED with a higher Vf will have a lower efficiency since it is running at a higher power. This means that the LED may run a little warmer than the average emitter.
Well, good luck with the testing! Please check your setup, and give us some more Vf ratings of your LEDs. It is informative to hear forward voltage ratings of LEDs like the XR-E where many of us purchase them (DX). It is a good heads up.
-Tony