Holly, this is a long time after your posting, but just want to share some info with you.

My dear paternal grandmother's maiden name was Schaer, and she immigrated from Switzerland in 1921. She was from the canton (state) of Aargau, which borders the canton of Bern. Because her parents died when she was very young and she was separated from her older siblings, I have also tried to find her family there, so far, without much luck. She was raised by her mother's brother, whose last name was Kunz.

I have been to Switzerland twice in recent years, and unfortunately, the name "Schaer" is about as common in the Bern and Oberaargau regions as "Jones" is here, so you may be looking for a needle in a haystack. Maybe by now, you have found what you were looking for. :-)