Gents,
NHBL's point about the rarity of mano a mano ship duels after the Age of Sail is a valid one. And yes, we needn't hear about all the exceptions, they simply prove the rule that major units rarely, if ever, deploy alone. Bismarck isn't going to encounter New Jersey on some sunny North Atlantic morning perfectly suited for a gun duel without either vessel having escorts and without aircraft being involved somehow.
A naval battle, as opposed to a "dream duel", is going to involve a number of details and the devil is in those details.
That being said, here's a short list of interesting naval battles that never happened:
American Civil War: The USN forces Charleston harbor and triggers one of the largest ironclad clashes to date. The Confederacy maintained a Charleston Defense Flotilla that consisted of as many as four casemate ironclads and dozens of contact-torpedo launches behind extensive torpedo (mine) fields and other obstructions.
Med in 1898: If Fashoda went "hot", both the French and UK Med fleets had very detailed war plans aimed specifically at each other. Such a campaign would see an "Old School/New School" clash as France's juene ecole torpedo boats and "storm of shells" met Britain's pre-dreadnoughts.
Canaries in 1898: In the Spanish-American War and after the Cuban campaign wound down, the US began planning an assault on the Canary Islands with the goal of seizing a coaling base that could support further naval campaign along Spain's coastline. Not all of Spain's navy had been sunk off Manila or Santiago, one ship in particular, the battleship Pelayo, was thought to among the best afloat, and the USN would be the one's far from home this time.
Sea of Japan 1905: During the 1940 Battle of the Yellow Sea, two very lucky shell hits on the Russian flagship Tsesarevich killed Admiral Vitgeft and killed or wounded all of his command staff just as darkness was falling. The Russian fleet then abandoned its attempted breakout and returned to Port Arthur, something that had seemed a near certainty until the shells hit. If Vitgeft had not been killed, the fleet would easily broke contact with the Japanese and steamed on to Vladivostok to await reinforcements from Europe.
Japan would then have been forced into a much harder blockade of a more distant harbor and the European reinforcements led by Rozhestvensky would not have been the desperate, send-them-all, grab bag of the OTL. Eventually, sometime in 1905 the Japanese fleet and reinforced Russian fleet would meet to determine who would control the Sea of Japan and the supply lines feeding the Japanese armies in Manchuria.
The Scarborough Raid: We've two possibilities at work in this one raid. Room 40 meant the RN knew about the planned raid almost as soon as the Germans did, but the usual C3I problems the RN suffered throughout the war meant that Hipper's battlecruisers escaped untouched. Making matters worse, the RN came within a twenty minutes of finding its 2nd Battle squadron under the guns of the entire High Seas Fleet.
A few tweaks to Beatty, Beatty's utterly worthless signals officer, or the 2nd Battle squadron commander and complete moron Warrender could have resulted in the destruction of Hipper. (Warrender's force actually had Hipper's light cruiser scouting force in sight and failed to open fire because Warrender had not received orders to do so!)
A few tweaks to von Ingenohl, the German C-in-C, would have mousetrapped both Warrender's 2nd Battle squadron. It wasn't as if the situation was confused either. Many German officers on the spot, Scheer was among them, realized that a golden opportunity was presenting itself and were livid when von Ingenohl turned away.
San Bernardino Strait: If Halsey hadn't sulked for a few hours over what he mistakenly perceived as a slight and what was in fact filler added to a message to make enemy decoding more difficult, he would have detached Lee and the 3rd Fleet's fast battleship force early enough to intercept Kurita and the IJN's Central Force before it could withdraw through San Bernardino Strait.
Kurita would have had 4 battleships, including Yamato, 6 heavy cruisers, and the usual mixed escort force of light cruisers and destroyers. Lee could have as many as 6 battleships of the Iowa, North Carolina, and South Dakota classes, as many as 4 heavy cruisers, and a larger number of escorts.
Thanks to several odd circumstances; like Halsey's carriers still chasing Ozawa's bait, the Japanese having so few carrier air crews left, and the Taffy groups off Samar still recovering from Kurita's earlier attack, this potential San Bernardino Strait battle would have had involved few aircraft.
Falklands 1982: When HMS Conqueror sank ARA Belgrano with two WW2 vintage torpedoes, that old cruiser was the southern part of a three pronged Argentine naval operation aimed at the RN task force. The sinking caused the other two Argentine forces, a center force consisting of the carrier Veinticinco de Mayo plus escorts and a northern force consisting of two SSM-armed destroyers, to withdraw back to base.
Of course, questions still surround just whether or how well the center Argentine carrier and northern missile boat forces was shadowed by Britain's SSNs. However, if those SSNs had been somehow given the slip, a very interesting battle could have happened.
Bill