#1
Hey. I bought a second hand ESP LTD H-351NT for £260. It is in exceptional condition aside from tarnish/rust on the upper frets and a little bit midway up the neck too. I'm assume it was kept in damp environment, or maybe something got spilled on it in storage... who knows..

Anyway, I've attached an image of the said 'tarnish'. 



Will this likely get worse over time? and is there anything I can do to clean it off?

Hopefully I won't need the thing refretting  
Main Rig
ESP LTD MH-350NT
Korg Pitchblack > Digitech Bad Monkey
Peavey 6505+ 112 w/ 2x12 (Celestion Vintage 30 and WGS Veteran 30)
[Effects Loop] Boss GE-7 > Boss CE-5 > TC Electronic Flashback
#2
Tarnish occurs on nickel frets over time, which is why it's beneficial to polish them every so often.

I use a piece of 8000 grit sandpaper. You could probably go a couple thousands of grit less fine than that and still be perfectly okay to use them for fret polishing. You can find sandpaper of grit that fine at an auto supply store. Check the paint section.

Alternatively if you want to overspend, stewmac sell fret erasers.

http://www.stewmac.com/Luthier_Tools/Tools_by_Job/Tools_for_Fretting/Fret_Erasers_Set_of_7.html?ShowMoreReviews=true
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I also have to do that. Cottaging this weekend
#3
I use Gorgomyte on mine.  That stuff is magic!
Guitars:
Jackson Kelly KE3 - MIJ (Distortion/Jazz)
Jackson DKMGT Dinky (EMG 81/85)
ESP E-II Eclipse Custom (JB/'59)
ESP LTD EC-1001FR (EMG 81/60)
Fender MIM Strat

Amps:
Mesa/Boogie Dual Rectifier Roadster 212
Laney IronHeart IRT-Studio
Peavey Vypyr 30
Peavey ReValver Amp Sims
TOOOO many T.C. Electronic Pedals. . .
#5
Quote by jedigovnaUG
What about a damp sponge? that might do it?


No.

Most people use 0000 (four 0's) steel wool to polish frets. You can get one of these things to surround individual frets and protect your fretboard:



These usually come in a set of two or three (a wide one and a couple of skinnier ones for the upper frets). http://www.stewmac.com/Luthier_Tools/Tools_by_Job/Tools_for_Necks_and_Fingerboards/StewMac_Fingerboard_Guards.html

You'll also want to put blue painter's tape over your pickups; the magnets will pull the tiny shards of steel into the magnets and onto the coil windings where they'll rust and cause your pickups to short out.
You can alternatively buy fret "erasers" from StewMac; they're designed to eliminate rust and polish your frets:

http://www.stewmac.com/Materials_and_Supplies/Sanding_and_Polishing/Sandpaper_and_Finishing_Papers/Fret_Erasers.html