I’m using Ubuntu 12.10, but this can be done with earlier versions. I’m also using Wine1.5.

First, you’re going to want to grab wine1.5, this can be done via the PPA.

Then, run: winetricks dotnet40 -q

This installs .NET 4.0 which EVEMon uses.

You can then run EVEMon.exe via wine:

wine EVEMon.exe