I am a head sacristan in France, so I only know what’s available in this country. However, a few years ago I had my pastor’s chalice and paten restored. This is how I went about it.
The first thing I did was seek the advice of a priest I know who had ordered the restoration of his own chalice and paten a few years earlier. I asked to examine the restored vessels and then obtained the contact information of the company that undertook the restoration. I then researched that company to determine their credentials and consult their references. Finally, I called them to schedule a meeting with one of their representatives for the inspection of my pastor’s chalice and paten and obtain an estimate of the work to be done. Shortly thereafter, we arranged the restoration.
A metal worker (silversmith, goldsmith, etc., depending upon what the vessels in question are made of), no matter how experienced and capable, is not sufficient. You want to find a company that specializes in liturgical articles, preferably as both a manufacturer and a refurbisher.
If you do not know of a priest or parish that has recently had vessels refurbished, you might try contacting the head sacristan of your diocese’s cathedral. Liturgical vessels in cathedrals tend to be very well looked after, so the head sacristan should know of a capable restorer or be able to refer you to whoever handles these tasks if (s)he does not do so himself (herself). If possible, ask to see something that has been restored within the past couple of years in order to judge for yourself the quality of the work. There is no substitute for being able to examine the result of a restoration with your own eyes and hands.
Though I can’t answer your actual question, I hope this helps in some way. Sacred vessel repair is rather expensive, so in my opinion it’s best to get help with it in real life. God bless!