Like the old analog meters, smart meters have a display showing usage. It should be a simple matter of recording readings to determine usage. There are lots of devices an electrician can use to record usage in the house. All he has to do is take measurements and compare the results. Then simply reconcile those with the electric bill.
I've seen this complaint a bunch of times. People claiming their bills went up with the new smart meters. Every bill shows starting and ending meter readings. Can't explain usage variations, but haven't seen anyone able to actually prove any type of overcharging yet.