Answer:
The same way that you test the tensile strength of anything - break it in a universal testing machine!
You have to be careful how you hold the rope though - you obviously cannot grip it the way you would grip a metal specimen (since the grips will cut the rope).
Therefore the rope may be locked into special rope-testing grips or tied around a T-bar or pin in a particuar way. As long as the rope breaks n the central "guage length", you have a good result. If it breaks in the region where it is gripped or tied, the result is probably not correct.