keep in mind that inrush current is pretty fast so you need a current probe with sufficient bandwidth.
transient protection needs to be measured in such a way that if the system fails to self protect, then your test method is not allowed to deliver desctructive energy.
for example, if you were measuring transient overvoltage, it would be good if you could apply a transient voltage yourself with known duration and then see if protective circuit works. if it does not work it is a good thing that you have applied a known duration transient.. the duration is obviously one that would be short enough not to cause damage. transient voltage can be created by charging inductors and then open circuit, you can charge a capactor and then close a contactor to have it appear in circuit.
in H-bridge, where shoot-through is a concern, you would command a mosfet ON for only 10us. the shoot-through protection circuit would have to self protect in less tine than that.. if it fails to protect, good thing your command signal was only 10uS!
see what i mean?