Sea power is a must for me. It gains importance I think when ironclads first appear. The ironclad is an effective floating seige engine. It will mow down any defensive units immediatly other than a musketeer or better. I build them along with troop vessels and soldiers, when the time is right, I can simultaniasly take a number of AI coastal cities. The ironclads blast away at any defenders and the boats land troops in disarmed cities. I go along the coast with my ironclad/ship/troop group and take over all the coatal cities. I usually start with cities away from the enemy's home continent. This way, I can halt their colonization efforts. After subduing the outer cities, my group travel along the coastline and take over all the coastal cities, at this time, I make sure that the enemy does not have either gunpowder or steam engine. Magnitism is annoying when frigates show up but not damaging to my force.
By taking all the coastal cities off-continent and on the continent, I have halted the enemy's expansion and made sure that he will be contained to that single continent. This obviously works better when the enemy is on an island continent and not overly expansionistic. In my last game the French fragmented their civ so much that I quited the game in frustration and started a new one. Now I do this to the Carthaginians with much better results... After I've cornered the enemy, it's a simple matter to muster enough ground force and/or dips&spies and close in on the ground cities.
I feel that the navy is most effective when you have steam engine & The Lighthouse before gunpowder and metallurgy is in your enemy's hands, and most useless in the trierme/caravel times. When the game starts, I don't bother with sea power, when Navigation, Magnetism and steam engine comes out, I take an interest, especially since steam engine gives me a way to "punish my enemies."-Military Advisor.
I am more or less clueless about naval warfare or sea power in the modern era though, does anyone have any comments and advise on that?