Or... you know on the shipyard you select the ship and say "Delete Design" It's not as quick and easy as the previously mentioned method because you have to wait until the design is available before you can delete it.

Obsolete a ship just removes it from the build list. If you want to remove a ship forever just click the "Delete" button in the shipyard.

And coming back and being available in future games is a much needed feature so you don't have to keep redesigning ships over and over again. But as I've gone through each game I've refined what ships I want and thus delete some old designs and make new ones of current ones. For example I've refined a series of small hulled fighter ships I've called "Scorpion class" which range from level 2 to level 5 attack of various beam weapon levels. Now I don't need to design any more small class hull ships from game to game again unless a special case comes up.

I think if you're playing a Metaverse game then the ships would appear in the Metaverse subdirectory.