Honestly, though my later-game experience is relatively limited, I'm not a huge fan of the navy OR the airforce thus far. Actually, I'm not too keen on the whole bombardment thing in general (though my governors seem to want these units ALL THE DAMN TIME). To get bombardment units to have my desired effects, I would have to use them in a LARGE tandem and then send the army in anyway. I know it's nice to use it to keep an enemy capital without roads and such, but that's really about it. I will use a smallish navy to transport troops to other continents D-Day style, but they just don't have the same kick for me as they did in Civ2.
I used to get hyped up when I saw a enemy navy units off my shores, but now I just keep a minimal navy to deal with these incursions and to intercept any transports. The roads and stuff can be rebuilt if they actually manage to bombard anything. Even mighty battleships can only bombard once per turn, and even then they still miss a bunch or just wound a defender. I find that I can take them out with destoyers if necessary.
I'd rather spend the shield on the most modern military units or an important improvement.