In theory, duty is due on goods over a relatively low limit. In my experience, the US customs seem to be uninterested in collecting duty on family property being sent to or brought in by a resident, so although you should be prepared to pay duty you may not have to pay anything, depending on circumstances such as how long your family has owned the plates.
For example, my late aunt left me her jewelry, all of which she had owned for decades. The total value was over $7,000. I am a British citizen and US resident, and brought the jewelry with me on returning from a trip to England. I filled in the customs form accurately, and was sent to secondary customs inspection. After questioning me for a few minutes, especially on whether I had bought anything new on my vacation, they decided not to collect any duty. I did have documentation with me - copies of my aunt's will, and of the valuer's report on her estate - but they did not ask to see the paperwork.
I suspect that experienced customs agents can distinguish someone who is telling the truth and has documentation to back it up from someone who is lying to them.
I strongly recommend telling the exact truth, and ideally having documentation to support it. Only claim you are returning items purchased in the US if that is what happened, and try to get sales receipts etc. to prove it.
The worst that can happen is you are caught committing a felony, lying in a customs declaration. That could happen if you declare, on a form or to a machine, that you have nothing of value and a search reveals a stack of silver plates.