Imagine a world with a dead core, like Mars, but covered in water. This world has managed to hold on to its atmosphere and quite a bit of its water as well. I'm sure the prodigious life there would be grateful if the planet could also hold on to its magnetic field.
This core has been dead for quite some time. In fact, enough time has passed for its surface terrain to be largely smoothed out from erosive processes like tropical downpours and waves.
We know that even on Mars, which has a mostly dead core that it still has localized magnetic fields. And Callisto has an induced magnetic field from Jupiter created by a subsurface ocean.
Can a world with a dead core still retain a respectable magnetic field?