The easiest way to measure total power output is to position the LED very near to a large photodetector.
You should be able to get large area photodiodes from: Vactec, EG&G, Hammamatsu, IPI Centronic, Optodiode, Silonix, among others. The last one is a Canadian co. Solar cells OK, but you should probably do a rough calibration. Here's one way to do it: Noonday sun at your latitude irradiates the surface of the earth with about 800 Watts/sq-m. This is equivalent to 800/10,000 = 80mW/sq-cm. Since Si efficacy for sunlight is about 0.5Amps/Watt, you should get around 40milliAmps for each square cm of solar cell. Supposing that you get a smaller value, then you can assume that your particular solar cell is less sensitive than 0.5A/W and calculate a calibration value appropriately.
Example: you obtain a 1"x1" solar cell, i.e., about 6.5sq-cm. At midday on a clear day, you measure about 200mA short circuit current max as you orient it toward the sun. You calculate 80 * 6.5 = 520mW incident on the cell, so you were expecting more like 260mA. This means that your cell has more like 0.38A/W efficacy.
I've glossed over some of the fine points, but all the above info is reasonably accurate