There exists such a thing known as the False Watermark. Unlike a Computer Watermark (which does not exist in paper), the False Watermark actually exists in paper. The False Watermark, like the true watermark, is apparent to a person looking at the paper in which it is created. The false aspect of the False Watermark has to do with how it is created.
John Mathieson, a Scotsman, produced counterfeit bank notes similar to those produced for the Darlington (England) Bank in 1778. Within the paper he had produced there was a watermark which was so clever and, according to Dard Hunter: "tallied so precisely with the original that no discrepancies could be detected." A number of papermakers studied the watermarks in the counterfeit bank notes and proclaimed them to be genuine. They were convinced that they were created in the normal manner in which watermarks were created, but Mathieson claimed that they were not. He maintained that he had devised a secret method to produce the watermarks, and that if he were pardoned he would divulge the secret. His bid for freedom was rejected by the authorities, and so he took his secret watermark method to the grave. The watermark produced by Mathieson was undoubtedly a false watermark.
A technique for creating a false watermark, which might have been the one Mathieson used consists of drawing a design on paper with a quill pen dipped in a solution composed of spermaceti (i.e. an oily substance drawn from the brains of a whale) and linseed oil of equal parts, melted in a water bath and then stirred till cold. Another recipe for a similar oily medium called for equal quantities of turpentine and Canada balsam, mixed together and agitated until the balsam is dissolved. Either of these two mixtures, when drawn on the surface of a sheet of paper will create a false watermark because the oil will cause the paper to appear somewhat transparent.
At some time prior to 1870, the Englishman, Walter B. Woodbury patented a photographic process whereby a transparent image could be created by manipulating reflected light. By reflecting light through a transparent positive image, a faint grey positive image would be created, which 'read' as a watermark.
Working independently, a number of individuals, including the Frenchmen, Davanne, Gobert, Jeanrenaud, Maquet and Marion, discovered another means to simulate a watermark without creating it in the production of the paper. They found that a "water-mark" could be created by pressing a blank sheet of paper onto a relief plate made from hardened gelatine. The resulting "water-mark" was a mirror image of the relief.
There is also a thing identified by the International Association Of Paper Historians (IHP) as being an official 'type' of watermark, which should more appropriately be categorized as a False watermark: the Embossed watermark. Embossing is performed on paper on the underside of the web (i.e. wire side) after the majority of the moisture is removed from the paper pulp. Rather than being created as a true watermark is, at the wet end of the paper machine, with a resulting modification to the density of the pulp fibers, and therefore variation in the opacity of the paper, the embossing process simply impresses a design against the surface of the paper.