The free School and Interests searches can help you find classmates. You just need to add the name of the school you both attended to your search. The search will return profiles of people who have stated that they are alumni of that school. You can then use other searches such as age, gender, or interests to narrow your search.
You can also try to find classmates by searching for common and shared friends. You can then search through the friends of classmates you are able to find to help you locate the missing classmate, as circles of friends tend to stay together.