RR Auction is an autographed memorabilia seller that has been in business for more than 30 years, selling more than 1000 items in each of their monthly auctions. The occasional Tolkien signed item has shown up, as seen in the table below.

RR Auction company website

Some notes on abbreviations used in these listings:

Hand written (ALS) letters are very much more sought after than typed letters - not just because they are clearly more personal and Tolkien spent more time on them, but also they are very much less likely to be forged.