Ok, the method #2 is to use a wardialer.
ToneLoc is the one wardialer I know of (the subject of wardialing is for another day), and I believe that ToneLoc had a remote modem identification. The way it works is it dials phone numbers, looking for modems to answer.
So, you download and install ToneLoc on your system. Then, configure it to dial the phone numbers of the modems of your remote systems. When it connects, ToneLoc reads the init commands coming from the remote modem.
If it has a match, it will tell you (again, I "think" it will do this) what kind of modem it is (as well as some other stuff that we won't get into at this time!). So, you can do it that way.
You will just have to make sure the remote systems are configured for their modems to answer an inbound call.
For more info on ToneLoc, including a download link to it, go here:
http://home.mminternet.com/~barneshouse/haq.htm