It's nearly the same as the tuning I use - so E minor is (from lowest string) 4;4(or open);4;open;2;2. The way I play with this system tho is,I would deaden the 5th.
You have a very nice E minor at the 9th fret too(without the 6th string) - 9;11;9;10;9.
There are a few around the 5th fret as well.