Are there pieces that would work by themselves, without the rest of the set? Perhaps a creamer and sugar bowl, or a serving dish, or a pitcher? Perhaps you could keep those (and pass them on to your children when they're grown), and then give the rest to a consignment shop or a thrift store. (If you give them to a consignment store, you're not going to get much money out of it; it's just an option.) It could be that someone else is looking for pieces to that set.
I'm sentimental about things, too. However, no matter what my emotions are, there is only so much storage room in the house!. So eventually one realizes the need to pass things on, hoping that other people will be delighted to have them.
By the way, if you can find repeats of the old Cosby Show on your television some time, you'll come across the episode in which Dr. Huxtable is sentimental about parting with his old water heater! There's another episode about a sofa. :^)