may be there are concerns and restrictions on using a normal multimeter the ordinary way
... may be normal meters don't measure correctly under certain circumstances. I will dig more about this. Seems an interesting topic to look at.
This is for sure, The current drain can vary in the operating cycle. As we are very much concerned with current we check the average current and the peaks as well. One simple way is to place a reasonable resistor in series with the power supply and look at the voltage drop with an oscilloscope. That will not necessarily be easy, as you want to keep low the voltage drop, but it can be done and give you a reasonable idea of what is going on. Choose the resistor as to get something between 10 and 100 mV drop. You may want to have a quick short circuit path to the resistor ( a jumper) in order to let the microprocessor start up, in certain cases this is necessary.