You'll need a cell phone with the GSM 900 and GSM 1800 frequency to be able to use it in Switzerland. GSM 1900 is the GSM band that can be used in the U.S. A tri-band phone (900/1800/1900) would be usable in both places.
We have a pre-pay phone here in Schweiz. Our cell phone is tri-band and we can switch out SIM cards to use in different countries. It's pretty useful for heavy travel. Otherwise, I hear that some of the Swiss contract plans are okay..though not that much less expensive, except the discount you can get on the phone.
http://www.telestial.com gives some useful information and I know this forum has addressed this often.
Good luck!
Jen