SWISS (LX) is a Star Alliance member based in Zurich (ZRH) and part of the Lufthansa Group. It flies across Europe and long-haul to North America, Asia, and Africa, with a polished business class and famously Swiss punctuality. One important rule up front: SWISS First class cannot be booked with partner miles at all. It is reserved for Miles&More elites, so business class is the realistic target.

Because SWISS is in Star Alliance, you can book its award space with partner miles, including:
The easiest place to search is the United Airlines website. United displays Star Alliance partner availability, including SWISS, and you can search without holding any miles.
Log in to your United Airlines account on united.com. If you don’t have an account yet, signing up is free.
Select the Book Travel box and fill in your trip details:
Then click Search.
Pick the flight option that fits your schedule. Watch the connection times carefully, as some options have very long layovers.
If you would like to search a different day, use the calendar to scan nearby dates. Zurich is a compact hub with quick connections, and space is usually better on the less obvious US gateways.
Make sure you select the Saver Award, as standard awards cost far more miles and usually can’t be booked with partner programs anyway.
Choose your preferred flight and open its details. Write down the following information: flight number, dates, and cabin class.
Now book with the program your miles live in. If it’s United miles, book right there on united.com. For other programs (Aeroplan, LifeMiles, Miles&Smiles), check their website first, since most can book Star Alliance partners online now. If the flight doesn’t show, call the program and read the agent the exact flights you found. They should be able to see and book the same space for you.