Is it possible to find the magma chambers that produce supervolcanos?
I am a seismologist, not a volcanologist, but we can use a method called seismic tomography to understand the size of magma chambers. 

This method is similar to a medical CT scan - the magma mush will have a slower seismic wavespeed than the surrounding 'normal' rock. Therefore, we can use this to determine the size of magma chambers from a tomographic image.

Even if a volcano does not appear to be active at the surface, it could still overlie a magmatic anomaly.

This approach was recently used to estimate the seismic of the Yellowstone magmatic body. See this paper: http://onlinelibrary.wiley.com/doi/10.1002/2014GL059588/abstract

Seismic tomography can theoretically be applied to any region, but we just need to have enough seismic sources nearby (e.g. earthquakes) to be able to do this accurately.