I would say that now your plum trees are old enough to fruit, you may have just been unlucky this year or last, due to other circumstances:
Do you know if they're self-fertile? Having two trees helps a lot, but self-fertile trees are known to produce a larger crop (especially when there are two in close range) and somewhat easier.
There are a few things I can think of off the top of my head:
Has there been a significant dry spell/drought in your area, this Spring? If they were under-watered during times like these, it can cause the trees to go into a sort of "survival mode", where they focus more on getting through the drought than setting fruit to reproduce.
Had you noticed any late, deep frosts, especially after the blossom/flowers had appeared? This can scorch the blossom, meaning that the fruit won't set.
(The above two are less likely as you mentioned your cherry tree is fine, though it depends whether they flowered at different times?)
Have you been adding feed/nutrients to your trees? Overfeeding can cause plants to grow excessively, producing lush leafage and wood at the expense of your fruit-crop.
Have the trees been pruned at all in the last 5 years?
If you can rule out most things, you may be able to establish why your plum trees aren't fruiting, and sort it for the next season. If it was a case of frost or drought, etc, the problem may fix itself and next year should be very bountiful!
Good luck; don't forget to let us know how you get on.