I'll guess the answer - Initially, only lateral separation will be possible. Then you have determine if the aircraft clear of cloud and in sight of the surface? If yes, provide an ATC service as appropriate. If not, you have to determine if there is there any other altitude information available. The Mode C might work when the altimeters won't and don't forget that many aircraft have some height information from a GPS. The RadAlt, if fitted may be of some help if you can vector them over flattish terrain. However, the thing to bear in mind is that the reason for lack of altitude information may be blocked static ports which means that all systems that rely on that information will be next to useless as well.
PM