I'm not sure if Classmates still works the same way, but it used to be that you could click on the name of the person you wanted to write. To actually write the letter, you had to be paid up, but clicking yielded the person's married name.
If you can remember your old friend's, parents', brothers' and/or sisters' names, googling on the old name may bring up a geneology site that will tell you her married name. The family names let you know you've found the right Mary Hatch. There could be many Hatchs, but only one whose mother's name was Sarah. Then it will tell you that she's married to George Bailey. From there, you google on Mary Bailey.
If you went to a small enough school, sometimes just writing to the school and saying you're hoping to get in touch with Mary Hatch from the class of 1968 will do it. The clerk might remember that Mary Bailey called saying she was hoping to hear from old classmates.
Also, try
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If the name is unusual, search all 50 states. If it's common, search on the state you went to highschool in. You'd be surprised how many people don't move away. A birth month and year sometimes shows up to let you know you've found the right person.
Despite all this advice, the bottom line comes down to its being harder to make friends later in life. I'm not sure what it is. Maybe we all get pickier or more suspicious. The only antidote is to keep joining things. Join a congregation, a quilt guild, a library book group. Volunteer. I finally got to where I started thinking of getting together with friends as a sort of job. That is, I meet someone I think I might like (from a quilt show we were both exhibiting in, in my gym's locker room when she was interested in the book on tape I was listening to, from walking dogs in the neighborhood, and another quilter), and schedule a lunch or get together with them (individually) once a month. I try to think of it like I do a job. Send email, await answers, don't nag, but do take it seriously enough to schedule the time and keep the commitment. I've never done that with friendship before. Everywhere else I've ever been at other stages in my life, friendship just happened. Now I plan, schedule, and follow through.
--Lia