If you're just going along the highway through the tunnel you can get a one day ticket for that part of the highway only for about 3 euros. I think it's called a "korridor" vignet. Beware though that the Austrian customs don't sell them as the Swiss do but you can get them at petrol stations either side of the border.
Don't be tempted to drive through without one, I got caught last year and ended up paying a 120 euro fine!
If you're coming from the Switzerland/Austria side it's easy: just don't get on the autobahn! If you're coming from the German autobahn (A96), make sure that you use the Lindau exit. If you miss it, it's too late.
We got our vignette just across the border from a petrol station. The cashier already had it in his hand ready so must have seen our Swiss number plate and guessed...
I know you can get the ordinary Vignette from the motorway services in CH leading towards Austria so I presume you could also get the Korridor too. You can't get them from the border crossing as far as I know.
Oops I did Zurich-Munich-Zurich this route earlier this year and didnt even know there was a toll.
Funny, if you go to Zurich maps for directions, Zurich-Munich uses the motorway but Zurich-Lindau uses the toll free route, even though the roads almost touch at the Lindau motorway exit.
We will be driving from Basel to the Dolomiti in October - we are planning to take a scenic route there - through Klosters but taking the motorway back which will go from Italy to Innsbruck in Austria before entering Switzerland. From reading this I take it that we will need an Austrian vignette? Is it easy to get one on the Italy side? We will be renting a car from Basel - is it possible that we can request the vignettes that we need - even is it is an extra fee? Or should we plan an alternate route?
On the AGIP on THIS side of the border has a sign posted on the door that says "NO KORRIDOR VIGNETTE". So unless you buy it elsewhere, it will have to be the €7 1-week regular vignette.
It is €7.90 for a 10-day vignette, which is compulsory for both motorways (A roads) and expressways (S).
When we drove through Austria on the way back from Munich, you can exit the motorway at the border and buy a vignette from a machine without getting out the car. If you didn't know that was there though, it would be quite easy to miss the sign.
I think that in Austria you also need to make sure you have an orange "high-visibility" jacket for each person in the car in case you break down and need to wait at the side of the road. My girlfriend is Swiss and she was certain we needed them. We picked them up at the first petrol station in Austria after the border.