Deciding which mouthpiece to use is difficult. This is a quick method of how to do it.
I have just finished testing 3 new Eb clarinet mouthpieces and thought I might share my method for what it is worth. This really involved 4 mouthpieces since I wanted to be certain the new one was better for me than my old one, also from a fine mp maker.
I first simply played on each one to get a general impression. I used the same music each time. You don't need to play every great lick you know....just something simple so you can listen. I used a reed that I considered to be very good, but not the best one, either, to see what the effect might be upon the reed. I then recorded each of the four mouthpieces with a digital recorder, put the recordings on my computer so I could listen to each in quick succession...sometimes only listening to a few notes to compare tone quality, ease of playing, and note stability. The music I picked had a lyrical part and a section that was challenging in order to hear how well the mouthpiece responded to those issues. Often the mouthpiece that seems to make it easy and fun for me to play is the best one.
I then used the Tuning Meister program that provides a graphical chart of each note played. For this, without watching the chart, I simply played a 2+ octave scale for each mouthpiece which was enough to fill a computer screen, stopped the graph, and then used the MS screen capture tool (snipping tool) to turn the graphs into a printable picture. I could then easily compare the intonation characteristics. While playing I did not attempt to adjust the notes, just played a simple scale. I am not quite done, since I will use the mouthpieces in rehearsals to see how they do in the real world. Tuningmeister can be found at http://tuningmeister.com/ Here is a sample of one of the mouthpiece graphs. I also did graphs using different barrels.