I have never seen the micro variation but there have been two classes of thing to link a GBA to the PC, and as the micro is electrically and protocol compatible with the GBA (it just lacks the GB/GBC capability so it has a slightly different shaped port to prevent the clueless from causing issues) they would work here as well.
1) Many years ago there was an emulator called VBA-link-real which functioned like a link cable between a PC and a real GBA. As far as I know the specs for the cable are lost and nobody has figured it out again, or made a new one, but
2) Standard multiboot cables, there are many of these but they all do the same thing and make it so a link cable goes between the PC (or some other non GBA/gamecube/wii device) and allows you to send a small bit of code over the cable and have it boot/run. There are a variety of cables out there
http://reinerziegler.de/GBA/gba.htm#Multiboot covers them and links to a few you could build too.
If you only want to dump GBA games and saves though then get a DS or DS lite (no dsi or 3ds as they don't have a GBA slot), basically any DS slot flash cart and a copy of rudolph's gba dumping tools.
http://filetrip.net/nds-downloads/applications/download-gba-backup-tool-0-21-f3228.html