A friend brought this video to my attention, and it show something people could try at home. This video shows an experiment in which a powdered carbon material (charcoal) is exposed to microwaves in a conventional microwave oven, and after 3 minutes or so demonstrates that it contains magnetic properties it did not have before being zapped.
Doing some more reading about this it seems that it is possible that the effect could be something other than carbon transmutating into iron oxide — since there is a known phenomenon that can make carbon magnetic. An article in Materialstoday.com explains:
Research has indicated that proton irradiation (i.e. hydrogen doping) of carbon can lead to the formation of ferromagnetic order. Scientists hypothesized that hydrogen atoms were incorporated into the graphite lattice during hydrogen doping, distorting the lattice and allowing the spins to align with each other.
I am not sure whether exposure to microwaves would allow such doping to occur. In the experiment above. I suppose that detailed laboratory analysis would be required to determine exactly what is going on here. Nevertheless, the experiment is quite interesting, and not beyond the scope of interested amateurs to carry out.