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Generally restoration starts at about $100 per piece. Often it is far cheaper to replace an item than to repair it.
Tarnish can sometimes be removed at home using baking soda and hot water with a polishing cloth. Here are the steps to go through: http://www.howtocleanstuff.net/how-to-polish-gold-trim-on-china/
Once the tarnish is removed, it's best to hand wash the dishes in the mildest possible dishwashing liquid. Unless china is specifically marked "dishwasher-safe" it shouldn't be put in the dishwasher, since this causes tarnish.
If you determine that the gold need to be replaced, then you could speak with a china restoration and conservator in your area. You don't mention where you live, so I can't search for you. However, again, repairs usually cost more than a replacement.
Please let me know if you have questions.
All the best,
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