Screen of a mobile phone inside something
The stewing pan should work. But at first the cover must be metal as well. At second, the stewing pan must be grounded. Not necessary to the phone ground. Some other ground should work as well - some water pipes (metal) or other metal, grounded part should be enough. Connect the pan to the ground with short and thick piece of wire.

I am not very sure how you will check the signal level in such a screen, because it is not transparent.