[Using a buck-boost converter]

Sorry for the late answer. I measured both units and they behave in a similar way - goes from low to high resistance on the input terminals.
However, I tested the other unit and it works perfectly. Seems to just be a faulty unit.

Thank you for your reply.

[Using a buck-boost converter]

I bought this little converter - a DM13B-3.3 which accepts a voltage range from 2.5 to 15V.

My problem is that it just seems to short circuit the battery - a 3.7V Li-ion. I'm positive (no pun intended) that I connected the right polarity. The unit got extremely hot in a matter of seconds and started to smell.

Have I misunderstood something very basic? The battery at Vin, 3.3V at Vout, right?

I have one other unit, but ask for advice, before I sacrifice that one, too.