I'm in favour of Huge Rocks. Personal preferrence, if you will. Also, no Bruce Willis around to stop it.
Just one little issue with Marburg's idea. EMP in Earth's atmosphere is generated by Gamma ray burst from nuclear based weapons cutting through Earth's magnetosphere. Would it then fry electronics in orbit? Also, what if they're using Optronic computers? Would it work?
Also, someone mentioned Non Nuclear EMP... I give you Paralyzer missile.
I guess the person to mention biological and bio based weaponry, as well as Jinx with nanites had hit the target bullseye. Release one nanite, or bacteria into the system, let it replicate itself and do your task.