Any idea what they were called? You would sign a document, press the ink, and then hand the papers to whomever needed them. Does this ring a bell?
Ink blotter.
Desk sets also could have sheets of blotting paper as a writing surface, so the writer could simply invert the page over the the blotter and press it down for a moment. This came from the age of pens and ink wells. You see "blot" as a verb..." writing in haste, she blotted the letter.." A hastily-dipped pen would have too much ink, which would flow out all at once, making a blot. The blotting paper writing surface eventually was replaced with fresh, when it became too blotted.