I would NEVER use Tarn-X on my Sherwood cups. Tarn-X is just too harsh - it contains thiourea (a leaching agent) and sulfamic acid (a strong cleaner that will remove rust!). I won't use a TarnX dip on ANY metals I care about.
In my experience, to polish the Sherwood Silver/Gold and Gold plated cups (including the chop cups), I use a mild silver polishing cream from the grocery store that includes a soft application sponge. I quickly apply this all over the cups, inside and out. Then immediately and thoroughly rinse with tap water leaving no polish on the cups and then dry and buff the cups with a non-abrasive cotton cloth. The result is a renewed luster to the silver and the gold plate with no tarnish. And don't make a habit of this either - once per year should be enough. Just handling the sterling silver will help to prevent tarnishing and simply wiping them with a clean cotton cloth will remove finger prints and restore a shine.
I would not use the chemically treated jeweler's silver cloth either. My rule of thumb is: if the cleaning agent or polish produces a black residue, it's too strong for plated surfaces. A jeweler's cloth (just like NevR Dull) will produce a black residue. These cleaners are fine for sterling but not plated surfaces.

Really, if you have Tarn-X in your home, throw it away before you ruin a valuable piece of apparatus - but that's just my opinion.
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Learn the form, but seek the formless. Learn it all, then forget it all. Learn the way, then find your own way.
Rings N Things / RNT2