Does anyone know what Dominant 7 or Diminished chord would resolve nicely to a minor key? i.e. Are there any Dom7 or Dim chords that would resolve to Em nicely?

Many thanks, Michal
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In minor, altered dominants (not specifically _alt) can sound really nice. I particularly find 7#5 chords to resolve really nicely to minor because you can hold the #5 as a common tone. 7b9 are pretty standard, though, the minor ii-V as immortalized in Stella: Em7b5 - A7b9
If you want diminished chords, you can form one on the 2nd, 4th, 6th, or (#)7th in a minor key. Up to you to decide what root sounds the best. The #7th has that nice leading tone thing going so that works. The reason this works is because it's essentially a V7b9 without the root. In E minor, a V7b9 would be a B7b9, containing B, D#, F#, A, C. If you remove the B, you get the same notes a diminished 7th chord formed on any of those aforementioned roots would've made.
Typically minor scales are altered to allow for a dominant V chord, and a diminished vii chord, which both do the same job as the respective chords in major keys.