Jupiter's moons, embedded in the magnetized, flowing plasma of Jupiter's magnetosphere, the plasma seas of the title, are fluids whose highly non-linear interactions imply complex behavior. In a plasma, magnetic fields couple widely separated regions; consequently plasma interactions are exceptionally sensitive to boundary conditions (often ill-specified). Perturbation fields arising from plasma currents greatly limit our ability to establish more than the dominant internal magnetic field of a moon. With a focus on Ganymede and a nod to Io, this paper discusses the complexity of plasma-moon interactions, explains how computer simulations have helped characterize the system and presents improved fits to Ganymede's internal field.