If you are interested in testing the accuracy of what current an overload will trip at, Zog's suggestion of using the NETA testing standards is the right answer. Do do it any other way is just barely better than an educated guess.
But if you are going to accept that an OL is going to perform as expected and you are looking for a FUNCTIONAL test, then what we would usually do on a motor starter is to test the control circuit (on a simplistic level if there is other automation involved) and also check that the OL relay functions to drop out the motor starter coil power. That's an important part of it, you need to ensure that the OL aux contacts are not welded or mis-wired, or a wire is not grounded somewhere etc. Most OLs have a "test" button somewhere. Some of the older ones however did not, or the test switch was not immediately obvious. it might take some digging.
