This example seems to be a very simple example of what you want:
Basically, you need to create an axes specifically for the colorbar (e.g. `colorbar_ax`) and call pyplot.colorbar(cax=colorbar_ax); or you can let mpl automatically take space from one of your existing axes: for example, pyplot.colorbar(ax=ax2).
You can also pass a mappable to pyplot.colorbar (in your example, cx1 or cx2), but by default, it will grab the most recently created one. Note, using the single colorbar for both subplots *only* makes sense if var_cint (in your code) is defining the *values* of the contour levels (as opposed to the *number* of contour levels). Otherwise, the colorbar will only be accurate for one of the two plots.