Basically, I've had this problem for a while, and I've started noticing it more and more.

When I mute my strings with my left (Fretting) hand, I get a lot of buzz and some harmonics managing to ring out, and I have no idea how on earth I stop them. They have a really nasty "Clang" to them and it's doing my head in

How do I get my mutes to sound like this (you guys will hate the song, but it's the best example I can find):


Around 30 ish seconds

When I go to mute, I raise my fingers off of the frets a bit. Could it be that I'm creating a load of harmonics when I do this? Am I using too much gain?

I can upload a sound sample/video if it's needed.
You actually need a decent amount of flesh on the strings or you'll get harmonics. Especially with high gain, but try and get more fingers on the strings before you quit. I don't understand why you'd be "raising your fingers off the frets" at all though, can you clarify?
Gah, I mean raising them off the strings so they're not touching a fret. I think I've got the technique right, I just can't stop this damn noise.
You keep saying "off the strings"... you just mean you stop fretting, but keep them on the strings, right? Try and get all 4 fingers flat across all 6 strings, that'll give you a good starting point - and then start turning down the gain if you still get noise.
Also pays to pay attention to what fret you're doing this on. 12th will be hard to eliminate sound on. 10th will be easier. Its all about where natural harmonics are.

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Try playing muted triplets (1-2-3, 1-2-3, 1-2-3)) with you picking hand while varying the amount of string muting with your fret hand until you find the "chuggida-chuggida-chuggida" sound you're looking for.

If you add a Wah and rock it up and down, you can emphasize it even more.