How to say replica as opposed to fake The only difference between a replica of a van Gogh painting, and a fake van Gogh painting, is that the replica claims to be a replica while the fake claims to be real.

This is a subtle distinction, and because people could feel insulted if I confuse the two, I want to be sure to get it right, and not just trust a dictionary.

So, if I want to buy high quality replicas of say, Ming dynasty furniture, how should i describe that in Chinese?   I do not want genuine historic antiques, and I certainly do not want to bother with people offering fakes as if they were genuine.  I want high quality replicas.

My concern is not talking with dealers.  My concern is when I ask a hotel clerk, or a shopkeeper who does not have what I want, where I might find what I want.  They should not think I am asking if they know any frauds or counterfeiters!
replica = 仿制品. 
 fake = 赝品

赝品 used to refer to replica that is very hard to identify whether it is authentic or not. As the language evolved, it refers to those with low qualities. 

So in Chinese, there is no direct mapping. Usually, you can add other adjectives to express the subtle meaning, like hello_harry suggested, 高仿, which is equal to 高级仿制品. 

赝品 also limited to those replica that trying to make the same as original and sell for profit. While 仿制品 don't have good or bad in the purpose, for example, 仿制品 can be made for museum, it can also be a different size. 

In your case, it seems you want to buy a  高级赝品 of furniture.