How much shielding does an ungrounded metal box provide? That is, a circuit is in a metal box but the box is not connected to either circuit ground nor externally earthed
Shielding generally works like this: If you apply an electric field from outside, electrons of the box material will start to move along the field direction. So, the one side becomes negative, the other positive charged. The field of this charges will cancel out the outer field totally inside the box, so there you will not measure any field.
Same applies for EM waves from inside / outside, the electrons in the box just have to move forth and back all the time.
However, it's not possible to shield an electrostatic charge inside the box, therefore, you need to ground it. (And magnetostatic fields can only be shielded by a ferromagnetic box.)
So, in general, a metal box will shield all EM waves and external electrostatic fields to some degree.
But if the mobility of the electrons is insufficient for the frequency of the radiation, they may not be able to follow the field fast enough, and then, EM waves may penetrate the box in either direction. Insufficient means: Too high resistance of the box / too high frequency / too high amplitude. So, to improve the shielding, use a thicker box, another nested box, or better box material.
Shielded enclosures typically also have a resonance frequency at which the shielding is poor (depending on how well the contents absorb emissions at the resonant frequency), and some small intentional or accidental apertures that can allow emissions to enter and leave. The shielding effectiveness of an enclosure is a function of many things.