My wife and I also eat gluten-free and we visited Zurich and other parts of Switzerland this past summer and this is what we experienced. Bear in mind that we are not celiac (although our daughter is), so we were not as sensitive to the risk of cross-contamination as someone with celiac would be. If you do have celiac, I'm sure you've developed an array of questions that precede almost any restaurant experience.
Having said that, in Switzerland you need to distinguish between breakfast vs lunch or dinner. Breakfasts are heavily bread influenced, but every place that we stayed in (including a couple of smaller pensions out in the country) were able to procure fresh-baked GF bread, provided the request was made by 5 PM (more or less) the day before. (The order is actually placed by them with the pharmacy, at least in some cases. Had no idea that pharmacists could also bake.) In many cases, the GF breads were the best we had ever encountered (and as SF Bay Area residents, we like to think we've experienced some pretty good ones in our local bakeries). We had visions of cracking the secret Swiss recipe for GF peasant bread and bringing it back to the States. Maybe in another life. The muesli tends to be unreliable, but some places do make a point to include GF muesli in their breakfast spreads and label it as such.
As to dinner, in Zurich, we did not search out GF-only restaurants (and doubt there are any), but instead merely avoided the fondue joints and the large touristy locales that can be problematic. We had a superb seafood dinner at Conti's (courtesy of a recommendation by Slowpoke on this board), but we also ate in several other places, just avoiding bread and noodle dishes, as well as anything with a heavy-looking sauce likely to have been fortified with yeast. Haus Hiltl (a vegetarian restaurant) was recommended as a good place for us, but we didn't have a chance to try it.
Outside of Zurich, we tended to eat dinners in our hotel restaurant, as they knew we were GF and always took pains to see that we had GF bread for dinner and even modified their main dish recipes on our account (thank you, Hotel Bellevue in Muerren!). Just dropping into a restaurant for dinner tended not to have such a successful result, and we'd often end up with just a salad.
As for lunches, since we're hikers, we either packed lunches from the hotel in the morning, or bought some GF bread and made sandwiches from the Coop. The packaged GF bread was actually also quite good (Scharfer, or something to that effect).
Last but not least, there is also a very good Swiss GF beer, although I'm no longer recalling the name. Ask about it and they'll know.
Hope this is helpful. Overall, we found it easier to travel GF in Switz than in the US. They're maybe not quite at the level of attainment of New Zealand in this regard (where apparently over 2% of the population has celiac), but very good overall.