I have a question.
Swords and armor were marked before or after hardening?

Ciao Maurizio!

I don't know medieval swords how and when were market, but later 19th century military swords were marked surely after hardening. Maybe the maker's mark or logo was stamped while the blade was still hot, but there are inspection stamps and unit markings which were stamped often in mobile workshops near the frontline where heat treating was impossible.
For example let's say a M1904 cavalry swordr. The blade was made and exported by Alex Coppel, Solingen the sword was hilted and assembled by Pacholek in Budapest inspected in Wien (Wn or Lw inspection mark) and some have multiple unit markings (the older ones were "erased"). It's unlikely that the blade was anealed and rehardened for each stamping. These markings are usually on the ricasso where the blade is much softer. I think the blademaker done all the heat treating process which was his closely guarded secret and later markings were stamped on the cold-stamped.

hi! i agree with this what was said before(stamps were on soft part of blade - ricasso, tang, or made before hardening on the blade) but i have another one idea. maybe sheets of steel were laminated and the surface where the mark is bitten is soft iron, and only core is hardened steel? like blade of the sword covered by the soft iron to protect from the break.

Part of the blade near the hilt usually was softer than the rest, right? To be more resilient at the stress point near the tang...