I will hazard a guess that this is *What Continues, What Fails* by David Brin (1991). It's not a perfect match -- the protagonist is part of a research team that is observing collisions of micro-black holes with a bigger one in order to observe things inside the bigger one, vs. waiting for one to collapse -- but the theme of universes spawning black holes which yield similar universes is a major focus.

A quote:

> Tides tugged at the camera, suspended between, and at the fibre-thin
> cable leading from the camera to her recorders. Peering into one of
> those pits of blackness, the mini-telescope saw nothing. That was only
> natural.
> 
> Nothing could escape from inside a black hole.
> 
> A special kind of nothing, though. Nothing that had formerly been
> light, before being stretched down to true nothingness in the act of
> climbing that steep slope.
> 
> The two funnels merged closer still. The microscopic black balls drew
> nearer.
> 
> *Light trying to escape a black hole is reddened to nonexistence. Nevertheless, virtual light can theoretically escape one nought, only
> to be sucked into the other. There it starts blue-shifting
> exponentially, as gravity yanks it down again. Between one event
> horizon and the other, the light doesn't "officially" exist. Not in
> the limiting case. Yet ideally, there should be a flow.*
> 
> They had not believed her on Kalimarn. Until one day she showed them
> it was possible, for the narrowest of instants, to tap the virtual
> stream. To squeeze between the red-shifted and blue-shifted segments.
> To catch the briefest glimpse --