Or perhaps you're asking about headset mics. Most good headset mics are condensers so they sound a bit different from SM58s. DPA and Countryman are known for quality headset mics.
Perhaps my post should have read:
What hands free microphones do you recommend for singing, while playing guitar so that I can move around the room, that would produce the same sound quality as the fixed Shure 58 on a mic stand for stationary performing?
Get a Shure drummer headset SM-10. Pretty standard if you want the warm dark close in sound. They're not the comfiest things but sound very similar to the 58
I have never had good results from a SM-10. Leave it for sports announcers.
I have had a good sound from Countryman Mics, but I have only used them for spoken word myself, I have heard them in use for an opera and they sounded great, but in both cases there was no stage monitors in use for the vocals.