Sweet cherry for zone 3/4 is almost not possible.

I can only think of a Evans pie cherry, allot less problem then
sweet cherry, good for jam / wine / and if you leave them on
for about another month after they turn red the sugar level will go up and lovely to eat out of hand.

When my Nankings get cherries, they've been delicious. Trouble is they don't always fruit, and we figure it's because of late frosts when the blossoms are on. This year we won't get any as it was -3 one night this past week. :( We do have two trees, but i didn't realize they needed pollinators. We had never heard that.

I have a Nanking in my front yard. It has fruited regularly for me, never have tasted them. I don't have another but it is an older neighborhood with plenty of fruit trees around the block so I can't say for sure it is self fertile. I think it is good on its own most of the closer fruit trees are ornamental crabs.

Even with zone-pushing, I think a sweet cherry in zone 3/4 would be a short-lived novelty. When I was younger I saw them planted in zone 5, and they did produce 10 or fewer cherries for a few years, then a hard winter would kill off the tree.

I live in zone 3 now and I have grown Nanking cherries. The fruit is rather small, seedy and okay to eat but is watery and has little flavor. A novelty, I'd get rid of it if you are looking for cherry production.

A better option is one of the "sour" or "tart" cherries. These are the cherries used for pie-fillings and processed cherry deserts. They are much hardier than sweet cherries and produce full-sized cherries, although I would again describe them as "okay to eat, but kind of watery and not a lot of flavor". They are semi-hardy in zone 3 -- a winter low of -30F (-35C) might do some minor damage to the plants, but -40F (-40C) could cause serious damage that the trees would survive, but it might take them a year or two to recover from. These are cherries such as Meteor, North Star, Montmorency, and Evans (Evans is sold in the U.S. as "Bali"). Evans (Bali) is the most productive and perhaps the hardiest of the sour cherries, hey it has survived in Edmonton Alberta for almost 100 years, so has seen lots of -40 winter lows.

Better yet are the cherries now being released from the breeding program at the University of Saskatchewan. They have been developing a number of cherry cultivars that can tolerate Canadian prairie winter temperatures of -50F (-45C), on an upright bush that grows 6-8 feet high and produces "sour" cherries that have as much or more sugar than sweet cherries such as "Bing", though they still retain higher acidity than "sweet" cherries such as Bing, Ranier or Lapin.

I bought 4 of the newly released U of Sask. varieties this spring, but they are still very hard to locate even on the Canadian prairies, and they may not yet be available in the U.S. or in Canada outside of the Canadian prairies. Here's a link to the breedng program at the U of Sask., so you can follow up...
http://www.fruit.usask.ca/dwarfsourcherries.html

Check out this site for the U of Sask Cherries.

Here is a link that might be useful: Honeyberry USA

I have a trio of Nanking cherry bushes growing on the eastern edge of my property, and they've borne a heavy fruit crop every year that I've been here in Peace River. The small fruit may not be as attractive to you as what you'd get from true sweet cherry cultivars, but I find them to be delicious, and often eat them straight off the bushes. I think they're well worth having on a city or smaller lot.