Those beads are doing something for you: they're blocking digital noise from getting back into the rest of your system. If you can keep them in you're doing yourself a favor.
When faced with this kind of work I prefer to use a digital scope, as it will give more meaningful information than a DMM and make for less-intrusive probing. As a bonus, the scope can also do lots of nice math on the waveform.
I suggest a couple probing options with a scope:
- "tombstone" solder the bead, then attach a sense resistor (0.1 Ohm, say) in series. Measure the IR drop across the sense with a differential probe, or use a pair of single-ended probes and do math on them in the scope to get the current.
To get better results, especially for low currents, I've sometimes used a lash-up of a good current sense amp (like the LT6105) in place of a diff probe to improve accuracy.
- "tombstone" the bead and put a wire loop on it. Use a clamp-on DC current probe. Make sure the probe is sensitive enough to do the job, since you're measuring tens to hundreds of mA.
Admittedly this isn't the best, since the MCU standby draw can get really small. And good, accurate clamp-on DC current probes are heinously expensive. You can improve the sensitivity of current probes by using multiple turns through the jaws; however the added wire length begins to have its own influence.
The sense amp lash-up I suggested above is still better as it's less intrusive. You can get one for the LT6105 here, from Mouser.
Either way, your scope will give you dynamic information on what's happening with the current draw, with better resolution than a DMM. And you can correlate current activity with operation state by using other signal traces on the scope.
Could you use the ferrite's DC resistance in place of a sense resistor? Probably not. The currents you are measuring are small, and the actual DCR value isn't known. (Not to mention that its impedance varies with frequency, which is kind of the point.)