Since I started writing historical fiction, I used contemporaneous paintings for my covers of those books. Initially, I found one by American artist John Singer Sargent. They were on the original covers for Roisin Campbell and A Studio on Bleecker Street.

When I began my Classics series, it made sense to search out paintings for the periods of the books, especially the Regency period for the batch of Austen’s. After they were up for a bit, I was warned that they might run afoul of the rights of some people, although they were in the public domain. I pulled the books until I could sort it out.A bit of research led me to a couple of things. This concerns the use of images made of artwork, generally by the institution that owns them.
First, although I’m not an intellectual property lawyer, my legal research makes it likely that if a museum takes a photo of a painting that is itself in the public domain and the photo is a “slavish copy,” i.e., it is an accurate image of the painting with nothing added (or subtracted), it lacks the originality required for a copyright in the U.S. I won’t get into my analysis but suffice it to say that while there’s only a single district court opinion on the subject–as it happens, in the Southern District of New York, which covers Manhattan, home of the Met–it wasn’t appealed and museums don’t seem to bringing claims, I think that they don’t sue about it because they’re afraid they’ll lose and then the lucrative business of getting people to pay fees for a license to use the image would die.

Second, it turns out that even if I am confident I can use images of paintings that are in the public domain, certain museums don’t force me to make that option. Under Open Access policies, a number of museums allow complete use, including for commercial purposes, of large parts of their collections. Generally they use the Creative Commons 0 license or, in the case of the Met, have an Open Access/Public Domain icon which leads to: “As part of the Met’s Open Access policy, you can freely copy, modify and distribute this image, even for commercial purposes.”
I thus spent time searching through collections of museums with Open Access policies for my covers. The institutions I use are the Met, the National Gallery, the Chicago Institute of Art, the Yale Museum, the Cleveland Museum, and the Smithsonian. (I’ve also redone the covers of my Gilded Age books.) (Though the Louvre is not a participant, Paris’s public museums are.)
I was clued into this by a blog post by Kathryn Goldman entitled Museums that Give Away Open Access Images of Public Domain Work.
An addition: On Facebook, Maria Yrsa Rönneus sent me a link to a 2014 article entitled The Public Domain vs. the Museum: The Limits of Copyright and Reproductions of Two-dimensional Works of Art, which provides a bit of an update with an emphasis on UK law. It notes that UK museums don’t seem to be in a rush to have the courts there decide the issue.