Thank you for the suggestions.
It looks like I might have spoken too soon though. I think the microphone on the older handset finally gave up.
It's completely dead now, I'm not hearing anything on the other telephone when I try to talk through it. The earpiece is still working okay, but nothing from the microphone. I tried tapping and shaking it and still nothing. I'm not sure what else to, so I guess I'll just have to try to replace it.
I found a few websites that sell parts for restoring antique telephones, and I saw a Kellogg microphone that looks the same as the one I have. (I hope they test them though, I don't want to end up with another bad one).
http://www.oldphoneworks.com/kellogg...r-element.html