I use a self-powered Sony stereo mike on a Sony MiniDisc recorder which delivers plug-in power and it works a treat - no damage to either machine or mike.
I'd advise against the smallest Sony stereo mike, though, as it's too small to stand under its own steam on a table-top without a large dollop of blu-tack or summat, while wearing it as a tie-mike with the little clip on the back means that you have to stand very still lest you record every rustle, grunt, belch and swallow. And it costs around £100, which is a bit steep for session recording.
Russ's solution sounds the best - two inexpensive mikes for different locations.