Elon Musk’s SpaceX completed an impressive, bicoastal demonstration of launch capability on Sunday, successfully executing the second of two unmanned missions within a roughly 48-hour period in a high-water mark for the company’s operational prowess.

Parts of both rockets returned safely to floating platforms, repeating what has become a signature feature of company launches. The back-to-backlaunches went off without a hitch, with all engines and navigation equipment performing as expected and the SpaceX team, for the first...