If you want to take a city (that's why you are blockading it right?), be quick and decisive. Bomb the daylights out of its defenses, then do an amphibious assault with marines, seals, or amphibious upgraded (Mech) Inf.
Alternatively, suicide a lot of artillery (without amphibious) and then ride in the tanks amphibiously (without the promotion, but that doens't matter anymore).
The fleet that was just threatening yours? Gone. The easiest way to kill ships is if they are still in port.
Basically, in the modern age, your first strike must completely cripple the enemy's war effort. Learn from the modern American military commanders in this.
Ok, so this is the same advice I'm getting from everybody. Basically what you're saying is you can't blockade. That's fine. I understand this.
But what if an enemy has more coastal cities than I can reasonably invade in a single turn? I might want to contain a fleet rather than letting it slip out to pillage my tiles, or run hit and fade attacks.
I think this question is worth answering and I'm still looking into it.
-- SJN