Spectral intensity distribution of supercontinuum must be measured with the help of spectrometer. I use Ocean Optics HR4000 mini-spectrometer with fiber input. Nothing can be simpler. Spectral range spans over all spectrum of supercontinuum. Large attenuation is, however, required to keep spectrometer CCD array safe. 

Depends on what else you want to measure. If you are working with a pulsed super continuum source, you in addition to measuring its spectrum, you might be interested in measuring its temporal intensity and phase: http://www.opticsinfobase.org/optica/abstract.cfm?uri=optica-1-2-119

Spectral intensity function of SC must be measured, of course, with a spectrometer of any kind. I use mini-spectrometer Ocean Optics HR4000 with fiber input. Nothing can be easier. Radiation, however, must be attenuated to keep CCD array safe. 

A spectrometer (Avaspec-3648, UK) can also be used for spectral analysis with integration times of either 10 or 40 ms. I have also used the HR4200 Ocean Optics spectrometer to measure the SC. I think these are the two simplest ways that the SC spectrum can be measured. 

Thank you so much for your suggestions, I ll  try with using OceanOptics HR 4000

I don't know whether it's true or not. I suggest that you use grating and camera. Focus the beam line on one horizontal pixel line. Use 2 different single mode laser beams as references. According to the location of these 2 beams on the pixels of camera you can estimate that each pixel corresponds to special wavelength.