I love using Black in combination with a wide range of blues from navy to the palest of shades. Most of the time a strong blue will be enough to create a pleasing counterpart to the black. But in cases where the two color palette is less than striking, try adding White in a small proportion to provide additional contrast, and unify the black and blue.
You can use Pure & Original’s Black and Soft Greek with highlights of White for the same look and finish as my cabinet below. Classico is their chalk based paint, requiring no primer, wax or sealer. Here, I wanted a very flat, matte, used chalkboard color and finish so I left my paint unsealed.