What is the last recorded instance of intentionally ramming a ship during a sea battle?

It depends on what you consider a sea battle. In the 20th and 21st centuries ramming has been used as a method of intimidation by forces seeking to maintain their own territorial integrity. During the Cod Wars of the 1950s-70s, several British ships were rammed by Icelandic ships. The Icelandic Coast Guard were seeking to secure Iceland's fisheries from British trawlers, while the RN sought to protect the British ships. Similarly, ramming was used by Soviet ships against American ones in the Black Sea, and by Vietnamese ships against Chinese ones in the South China Sea.

The last cases of ramming during a declared war occurred during WW2. On the night of the 6th-7th April 1945, British MTBs and German E-boats clashed off the Dutch coast. One British MTB, M.T.B 493, rammed an E-boat, while another, M.T.B. 494 was itself rammed by an E-boat. 494 was sunk, and 493 was not repaired, while one E-boat was sunk. However, this was a small craft action. The last case of two surface ships ramming each other was that of the British destroyer HMS Glowworm in April 1940. Glowworm had been operating with HMS Renown to cover minelaying operations off the coast of Norway. She was detached on the 7th April, to recover a man lost overboard in heavy weather. While attempting to rejoin with Renown, she encountered German forces moving into position to invade Norway. Heavily outnumbered, she rammed the German heavy cruiser Admiral Hipper, before sinking. Hipper was heavily damaged, but was able to continue her mission. However, it isn't entirely clear whether or not this ramming was deliberate. It may have been caused by damage to the bridge or rudder preventing her from avoiding it, rather than by conscious action on the part of her commander. To find the last definitively deliberate attempt at ramming between surface ships in a naval battle, we have to go back to the Battle of Jutland in 1916. During the confused night action after the main fleet clash, British destroyers closed with the German fleet, in an attempt to prevent them retreating to the safety of its base at the Jade. During this, the German battleship Nassau attempted to ram HMS Spitfire. Spitfire had slowed to deliver assistance to another member of her flotilla, and was an easy target. Fortunately for her, she managed to avoid a full collision, instead scraping down Nassau's side. She lost 60 feet of plating, but was able to return to base. [Her superstructure](https://en.wikipedia.org/wiki/HMS_Spitfire_(1912)#/media/File:HMSSpitfireJutlanddamage.jpg) was completely demolished by the blast effects of Nassau's guns, which couldn't be depressed enough to hit Spitfire.

Ramming was also used in both World Wars as an anti-submarine measure. Several U-boats were sunk by ramming, including one by a merchant ship. SS Scorton rammed U-633 on 10th March 1943, successfully sinking her. A rammed U-boat was also the only ship sunk by HMS Dreadnought - U-29, commanded by Otto Weddigen who had sunk four British armoured cruisers in September-October 1914, including three on a single day. However, ramming submarines could often cause heavy damage to the rammer, as well as to the rammed, with HMS Easton having to spend 11 months being repaired after ramming a U-boat in 1943. This led to the RN strongly discouraging the use of ramming from mid-1943.