What is an appropiate way to isolate a DC signal?
I can suggest two solutions. If the isolation can be less than perfect, meaning many megohms in the ground path, use an op-amp in differential mode for the DC signal input side and drive the black box with the ground and output of the difference amp.

For total isolation you can use optical much like the digital. The light (LED) brightness is controlled by an op-amp with an optical detector in the feedback. The same kind of detector is used on the isolated side and a simple calibration can correlate the two detectors. Check figure 3 here  http://www.digikey.com/en/articles/techzone/2012/dec/linear-optical-isolation-for-safe-sensor-operation and these are the high end units   http://www.ti.com/general/docs/lit/getliterature.tsp?literatureNumber=sbos129

Transformers are also still used of course.  http://www.analog.com/static/importedfiles/tutorials/MT-071.pdf