Generally, it would work the other way around - you'd have to prove your lineage by applying the oldest method to do so: subjecting yourself to/providing a so called "Adelsprobe" or "Ahnenprobe" (proof of nobility/proof of ancestry). To do so, you'd have to furnish at least part of your pedigree/family tree and provide names and escutcheons/coat of arms for several generations of your ancestors. These claims (you or whoever else is next down the tree being a descendant of each particular noble person) would have to be confirmed by oath by the current head of the house/branch of house of that particular ancestor; or in some cases (much more frequent as time went on) by other peers of equal rank. A picture of what an Adelprobe looks like can be found on the corresponding German wiki entry (unfortunately in German only) here. The single escutcheon on the bottom is that of the proband, the pair above are his parents, the row above them his grandparents and so on. These "attested family tree"-style documents have existed since the High Middle Ages. In conjunction with an Ahnentafel, this offers a pretty definite proof.

Furthermore, If we're talking 18th century and "very royal blood", you'd have to appear on the pages of the Almanach de Gotha, and/or similar almanacs of european nobility.

If you manage to come up with a colorful explanation of why you(r direct ancestors) don't feature there (estranged, babies swapped, born out of wedlock as the result of an affair - that kind of thing), you'll be very hard pressed to find anyone who'll believe you, but could try to apply directly to the "next in line" noble ancestor and entreat them to back your claim of kinship to them by oath. That is romantic literature/dime novel territory, though, and very unlikely to get you the result you hope for - you'd be much more likely to be investigated/charged as a fraudster/swindler by your noble "relatives".