Not just two battleships- the Scharnhorst and Gneisenau, as well as the Deutschland-class "pocket battleships," were part of Germany's modern capital ship fleet.

The Germans knew they could not come close to achieving parity with the Royal Navy, and instead had several reasons/strategies for their capital ships.

1. Temporary local superiority for naval operations. The invasion of Norway in April 1940 is a good example of this. The German navy landed troops in Norway while avoiding direct action with the bulk of the Royal Navy. There were two naval battles in Narvik fjord- one of destroyers attacking destroyers and another between a small British task force with the British battleship Warspite and carrier Furious attacking a German force of destroyers. Even though the Royal Navy won the second of those battles, it was unable to do much about the initial landings and Britain subsequently lost the Norwegian land campaign. In June 1940, as Allied forces were withdrawing, the British carrier Glorious was even surprised and sunk by gunfire from the Scharnhorst and Gneisenau. While the German surface forces couldn't engage the whole Royal Navy, they, along with the Luftwaffe, were enough to temporarily take control of some areas, at least initially in the war.

2. Propaganda. Battleship production was one of the lead arms races in the build up to the first world war, and 20 years later capital ships were symbols of national pride and of the vindication of German rearmament. Political/social history isn't my area, so I can't comment on specifics, but the Bismark and Tirpitz were both launched with lots of fanfare and dignitaries in attendance, also Hitler himself I believe.

3. Commerce raiding. This was the principal military value of the German surface fleet, at least in theory. The vision was one of these German capital ships being unleashed upon the defenseless British convoys. The aforementioned pocket battleships, built in the 1930's, were intended as pure commerce raiders because of severe early treaty restrictions. Too many trade-offs hampered the design a bit in hindsight, such as a lack of speed, but the idea was to put battleship-caliber weapons and battleship-grade armor onto a small, two-turret vessel equipped with diesel engines instead of steam turbines for fuel economy. The Admiral Graf Spee had quite a bit of success in the first few months of the war around South America before it was sunk in December 1939. The idea had a bit more merit with the faster, more powerful vessels. The Bismarck was sunk not just "sailing up and around The British Isles," but while trying to "break out" into the Atlantic to devastate any convoys it came across and use it's speed/surprise to escape if encountering superior enemy forces. Fighting the Hood/Prince of Wales was not the direct mission, but was self-defense whilst trying to escape to the Atlantic. The Scharnhorst was sunk later in the war during a similar commerce raiding mission against the Arctic convoys. All told, you are correct in that the German surface fleet did not represent a good return for the investment, but that is with the benefit of hindsight. The threat of German commerce raiders tied up a large fraction of the Royal Navy's resources that could otherwise have been used in places like the Mediterranean, where the Italians had a strong surface fleet. There were even instances where the threat of attack from German surface vessels had a great impact, such as the convoy PQ17. In mid-1942, this convoy dispersed when the British received erroneous reports that the Tirpitz was on its way to engage, and subsequently lost 24 out of 35 of the scattered, isolated merchants to German submarines and aircraft.

Bismarck and Tirpiz were laid down in 1936. Their construction was started before the war without knowing when exactly the war would begin, who it might be against, or what naval strategy would be employed. When they were laid down they were to be part of a small group of German capital ships along with the Battlecruisers Scharnhorst and Gneisenau and three "pocket battleships" (built under Weimar.) A small squadron of capital ships would be able to dominate the baltic sea in the event of a conflict with the Soviets, or perhaps contend with the French navy in the Atlantic while the Italians contended with them in the Mediterranean. It was not known that a war with Britain and the Royal Navy would ensue, and against other opponents the Battleships might have proved decisive.

Additionally German heavy ships (cruisers and up) did have some early successes during the war. They facilitated the invasion of Norway in early 1940, covering transports and disrupting the British counter invasion. Scharnhorst and Gneisenau sank a Royal Navy aircraft carrier during this campaign. They had several successful commerce raiding actions against convoys in the first few years of the war, and occasionally were used in Norway against baltic convoys in the later years. By 1943, Hitler had realized these ships were no longer effective and had reallocated the resources needed to keep them combat ready.

Also, despite the lack of successes in pitched battles, the German Capital ships did have a substantial impact on the war. They forced the Royal Navy to keep a fleet of battleships constantly on call to defend against a sudden outbreak. Convoys sailing from Halifax had to be escorted by old battleships to defend against a German heavy ship sortie. This exposed these ships to submarine attacks. Because the British could never risk a naval disaster in the North Sea, the British were unable to bring their full naval power to bear in the Mediterranean or (later) the Pacific theater but had to keep substantial fleet elements at home. As long as the German capital ships were semi-operational, hiding in port, the British did not dare reallocate naval resources.

Ultimately, the large battleships really were a waste of resources. The advance of Air and Submarine technology made them a bad investment. However the Germans were not alone in making this bad investment. The Americans, British, Japanese, Italians and French had made the same decision to construct battleships at around the same time (late 1930s.)

I live in Tromsø where the Tirpitz was sunk, and in school we made knives out of the cannon barrels. My woodworking teacher at the time claimed that the barrels were made out of steel of such high quality that it would cost the GDP of a minor nation to cast them today. Is there any truth to this claim, I am sceptical myself.

In addition to the above posters, I want to add that military thinking on all sides at the time hadn't yet decided that battleships were less useful than aircraft carriers, which began competing for space in navies all over the world. Japan used aircraft carriers to great effect at Pearl Harbor but their strategy was to destroy the US battleship contingent. They didn't realize how important American carriers were til later. It took the Americans a while to understand the advantage of carriers too, but that began to thaw in the interwar period a time when-was it Gen Mitchell? I forget- demonstrated an aircraft attack on a decommissioned navy ship to justify its utility.

The Dawn of American Airpower is a good book on this subject.