Surprising what happens if you have some contaminant stuck on one of the rollers of a laminating machine and you just happen to put through a piece of paper with a damp area.
I might be wrong but I *think* the watermark was one of those accidental inventions.
It certainly would not be suitable for anything too naughty that needed precise placement but if you are happy for a "near enough" approach, you could experiment along the following lines.
Purchase some adhesive THICK copper foil - and also some laser printed etch resist etc - and create an etched foil (already stuck on the roller). You will now have a raised and reasonably hard logo on the roller.
If you do not need too many impression you can increase the height of the metal by wiping it over with a powerful soldering iron and low melt solder. A powerful iron and low melt solder means heat need only be applied for a second or so to any one area - so the roller should not be harmed. If this results in a grey mark on the paper (from the lead) then a heavy coat of lacquer will soften the edges (lose detail) but will stop the metal marking the paper.
Re assemble the laminator and dampen the area of the paper you want to be watermarked. Experiment with both the cold and the hot setting.
You may find that even on dry paper it may make a weak watermark - but where the paper was damp, then the watermark should be reasonably clear if you used a fairly thick foil and the rollers are tight. If the images is too weak, put the paper through with a sheet of thick card on the back - it will increase the pressure on the paper from the metal design.
Experiment and play around a bit.
A REALLY crude way but works (in a fashion)if you have a simple logo that can be "one piece" of metal without needing a backing, then get a block of wood (or other firm smooth surface), place the paper down, then the metal logo design in the correct place (pre-damped) and then cover this with a sheet of regular cheap paper. Press down HARD with a domestic iron.
Experiment with temperature - from cold to VERY hot, different pressures and different time.
Certainly when transferring images in the past when I didn't want any "watermark" effects, I would sometimes notice that the cover paper (the cheap one to protect the transfer) would end up with a "watermark" if there was any creasing or other foreign material between the paper and the iron.
In both cases, (roller or iron) the initial result will be a recessed design. This then needs to be flattened back out (plain roller / iron with no metal design in the way) and you should then find the design can no longer be felt and barely seen UNLESS you hold it to the light.
If the needs are reasonably modest, some kind of watermark is not too hard to do have fun and play with.
Damp paper, a metal "thing" to press on it and a form of clamp/roller or press should give you some results which may suffice at a push
