Is it possible to save/preserve cherry pits with the intent on planting them later?

I have an old cherry tree on the border of my property and my neighbor's.  I don't know the age, but the tree is pretty old.  I figure it's a real tree, not some geneticly modified, possible sterile hybrid.  Last year's cherries were awesome.  I'm hoping to move soon and plan on having some fruit trees in my future home.

Thanks as always.

Why not just save the whole cherries pit and all?

Or start pits in some pots so they can start growing that way you'll can tell if you need more?

Try to start some and see if they will grow.  You will still need to transplant them later and wait a few years to see if they will bare edible fruit.

I understand that cherry trees have to be grafted (like apple trees) to reliably bear quality fruit.

BUT you could start by growing a cherry tree and graft a limb onto it.  (Admittadly I have no experience with this).

There's no way of knowing what quality fruit you'll get if you plant seeds, and it'll take years to find out. If you want to get the fruit that tree bears, the only way to guarantee that is by propagating that tree.
It's not that hard to propagate many fruit trees from cuttings. Cherry trees seem to do best with branch tip cuttings. If you want to get some of THOSE cherries, you should take a bunch of cuttings from the tips of the branches, put them in some pots of potting soil, and mist them several times a day under a small plastic tent(out of direct sunlight).
You might check the original tree to make sure it doesn't have a graft junction near the ground. If it does that variety of cherry might not be hardy enough for your area, and you'll have to graft it onto a hardier rootstock.

I would start planting them now and see what happens.  It will take about 5-10 years before you can get fruit so no better time to start then now  

As a kid we planted a couple pits from Georgia peaches we bought at the grocery store.  The pits germinated and grew and in a few years we had some of the biggest and best peaches you could get anywhere.  The trees are still alive today and I will guess they are 30 to 32-years old now but it did take quite a while before we got anything from them.