score:4
I did a lot of googeling during the last few days and I finally found a more or less cheap flight. It seems that Intersky has regular flights from Zurich to Elba. Unfortunately I couldn't find these flights neither on ebookers nor on some well-known matrix flight search engines.
However, Interksy offers flights starting at 112 Euros. So it is cheaper and faster than taking the train.
Upvote:6
The train station to look for is Piombino. From there, walk to Piombino Marittima where the ferry starts.
I found a ticket train from Zurich to Piombino at CHF 258. I don't know if it is the cheapest.