I reproduce some instructive quotes from Reddit. To ameliorate readability, I eschew blockquotes ``.
hassh 2 points 2 months ago:
http://www.similarsong.com (site down 05/2017)
lvav68 1 point 2 months ago
I don't feel Pandora is that
well [good] for me it can get random. Try last.fm, I tried it once and worked well [...]
[...] Failing that, I look up the artist on a bunch of different sites to try and pin down the genre. If you can figure out the genre, it makes it a lot easier to find similar artists. Try
[...] Let's apply this process to the song you posted. First, I checked last.fm. Nothing. Discogs and Musicbrainz also don't turn anything up, so now we move on to Google. Aha! Found Gavin's reverbnation page! He lists himself as "Other / Film Music / Cinematic Instrumental", so we'll search last.fm for stuff people have tagged as "cinematic". Bam. There's some similar artists.
Now, if you're already reasonably educated about genres and their sounds, you can always take a stab in the dark at similar artists. When I first heard the song you linked, I thought it sounded distinctly New Age. So if you check the last.fm tags for "New Age", you'll probably find some more similar artists. Hell, the description is "New Age music is music intended to create “sonic spaces,” conducive of artistic inspiration, relaxation, and optimism. It is used by listeners for yoga, massage, meditation, and reading as a method of stress management or to create a peaceful atmosphere in their home or other environments"—doesn't that sound exactly like what you were looking for?