Thank you all for your responses. I am troubleshooting an ATAG induction cooking plate. It has blown one of the PCB tracks during cooking ... The track was meant to blow as a fuse. I found a short on the circuit and replaced the shorted part (a relay). but the thing still refuses to work correctly. I did poke around with oscilloscope a bit while it was connected in its place, but it is not exactly comfortable to work in the kitchen. So I took the whole thing to my bench and now struggling on the safest way to connect it.
Thanks for pointing out the GFI or residual-current device (RCD) ... totally forgot about those. Indeed, if you have those installed in your home, then it is highly recommended mandatory to ground everything.
But the best idea to date, i guess, is to get an isolation transformer. By the way, the medical grade transformer will also do good (as usual - my amateur opinion, NOT a fact), BUT you will have to modify it first. The mod is simple - cut off the ground wire going to the secondary coil of the transformer. By doing that you de-reference the secondary coil from the ground.
I am using a Rigol DS1052E to probe around.
If I have a ground lead connected, I remove the ground lead from my probe, so it does not touch anything by accident. In case I want to do differential measurements, I would use both channels on my oscilloscope and a Math function to get the difference.
Perhaps off-topic:
I do not have an ESR meter, but I try to get around with my signal generator (to generate 100kHz square) + oscilloscope to measure voltage drop. Gives me (I think ... please tell me if I'm wrong) a rough indication of ESR. If square wave flats out - ESR is low ... The higher the amplitude of the square wave, the higher the ESR. Right?