Paper money is catalogued by Krause Publications. The books are heavy and relatively expensive, but I believe at least some are available electronically. There is no comprehensive web site, like numismaster, for banknotes.
My own solution is that I have nagged the nearest public library to buy the books, since I seldom need them. The library agreed and it proved to be a popular book, so now they are buying the latest edition of the whole series. My next step will be to convince them to sell me the old editions.
Peter