Since I just spent about half an hour trying to figure out what's the problem with the white space around the exported images (EA Version 9.3.935) I thought I'd sent an update to this old thread:
When exporting to EMF using "Diagram->Save As Image", EA seems to take the Windows System: Display resolution options into account. In order to adjust to working on my small notebook screen I had the field "Change the size of text, apps, and other items" set to 125%. This seems to be the cause of the extra white space around the exported figures.
In order to fix it, go to the Windows Settings->Display->"Change the size of text, apps, and other items" and change that field to 100%. Close the settings, and export your figures from EA.
Hope this helps!
-markus