One way to go might be a decent quality condenser microphone, rather than a dynamic mic like the SM58 and the like. I've used an AKG C1000S for mandolin; not too expensive, robust and decent sound quality. Needs a 9v battery, or will work off phantom power. Simon Mayor uses condensers rather than pickups, and gets great tone on mandolin and guitar. Check out ebay, there are usually quite a few around.
Tim from Bit on the Side