The grandparents' plates is correct. I am American and what I was taught is that the plural possessive requires an apostrophe after the s. The singular possessive has an apostrophe just before the s (the grandmother's plates).
I wrote "these are the plates of the grandparents" which is kind of a literal translation, but we would never say it like this in English. Correct: "These are the grandparents' plates." The apostrophe comes after s because it is plural posessive (i.e. belongs to more than one grandparent)