Does anyone have an idea how I could go about selling a small limited-edition etching by a very famous 20th century artist, that doesn't involve internet auction sites?
Take it to a 'proper' auction house . They are in every large town.
In addition to the well known ones like Sotheby's there are 100s of smaller ones. But if it really is by a very famous artist then go to one of the leaders like Sotheby's as they have a larger database of possible buyers. If it is not suitable for them they will suggest an auction house that is a better choice.
It cost nothing to ask their opinion.
Thanks, Eddie. Difficult for me to get to London, but I think somewhere like Sotheby's or Christies will probably be the best bet. Maybe I could try emailing them a photo with other details.
Sotheby's ,Christie's, and Bonhams have branches all over the country , you do not need to go to London to see them. In addition all the cities and many large towns have their own auction houses. These auction houses can arrange to sell items on commision at other auctioneers if they think it will get a better price.