Given this is such a specialised application (why do you need to do it in the first place?), you would be better off looking at the literature available from the associated testing equipment supplier's websites.
It is difficult to answer your question, unless your exact product details are known? What rating super capacitors do you need to test? Do you intend to manufacture super capacitors?
standard capacitor testing equippment will work, these are, after all, capacitors.
They are smaller in size for the same capacitance as the older styles, they are often lower in voltage, but some are made to be high voltage to allow the 1/2CV2 to give you as much stored power as you can get.
Even so, a discharge through a fixed resistor will allow you to characterize them.
I hear they are not tolerant of over voltages, and you may ruin them with spikes which can cause their destruction via internal dischharge.