Magnetic fields on early Earth, Venus, and the Moon may have been generated or influenced by basal magma oceans (BMOs)—molten silicate layers above their metallic cores. To investigate this possibility, we performed 3D dynamo simulations with strong core–BMO contrasts in density and electrical conductivity and examined scenarios with convecting BMOs, convecting or stratified cores, and the presence of an inner core. We find that BMOs alone produce weak fields, but stronger, dipole-dominated fields arise when both the BMO and core are convecting. These results help assess whether BMO-linked dynamos could explain paleomagnetic observations from rocky planetary bodies.