 If you liked
Shinsekai yori
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 ...then you might like
Re:Zero kara Hajimeru Isekai Seikatsu
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These series both explore supernatural psychological themes in a way that captivate their audience. While Re:Zero is focused on a style that combines fantasy, comedy, and dark events (meant for a less mature audience), Shinsekai Yori is a more realistic version of a psychological anime portayed in a rather serious way (meant for a more mature audience). The dark themes in common to both are interesting to watch so you will probably like the other. Both are masterpieces, but for different audiences.
Similar overall feelings. Supernatural powers involved as well as how to make good use of them, fighting tactics etc. Music that suits perfectly to the atmosphere and mastered animation with cool effects. Sometimes you'll feel as lost as the characters. Almost same approach of mystery and psychology.
These two series have moments that can give the audience psychological shocks (in different ways). Both Shinsekai yori and Re: Zero focus on supernatural aspects and have dark themes (Shinsekai yori is a lot more darker though). These two also have heart warming moments. Besides, these two series have wonderful art, music and scenes. The world-building concept too is Awesome!
This recomendation pretends less to the actual themes of the series, and instead the feeling of hopelessness and deperation it instills at times. If youre the type of person who can enjoy a series even tho it makes you feel uneasy and sad at times youre probaly gonna be able to appreciate both of them.