 If you liked Mononoke Hime |  ...then you might like Karigurashi no Arrietty |
First off they are both by Ghibli studios. So they both have that same magical feel, with beautifully animated art. Some form of nature is represented in both movies, filled with fantasy like aspects.
With most recommendations already, and mine, there is a Ghibli connection here. Though Secret World and Princess Mononoke have their intimate similarities such as a strong female lead who does everything in their power to better their family. A dude comes along and aids in such a mission as well. You could look at both as two sides of the same coin in some respect. Both are great Studio Ghibli movies, for all to enjoy.
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