Em wave going into metal.

A metal box will block most EM waves. Is this because the oscillating E field
will be canceled when in contact with the conductor. And because the oscillating E field
is the source of the changing B field does this then kill the B field.

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 Good conductor attenuate the EM wave, don't necessary block the EM wave. It depends on the thickness and the frequency of the EM wave. For good conductor: $$δ=\alpha+j\beta\;\hbox { where }\; \alpha=\beta=\sqrt{\pi f \mu σ}$$ Attenuation is $$e^{-\alpha z}=\frac {V_{out}}{V_{in}}$$ As you see, it is frequency and conductance dependent. Set the thickness z in the equation to get the desired attenuation( Vout/Vin). http://en.wikipedia.org/wiki/Skin_effect
 it is not true that metal plates will block EM waves.it depends on the plasma frequency of metal,if it is below the incident frequency there will be transmission of EM waves. http://en.wikipedia.org/wiki/Plasmon

Em wave going into metal.

If you look at the formula, the lower the frequency, the thicker the metal has to be to block the EM wave. In guitar magnetic pick call Lace Sensors, they are known to be lower noise than other regular single coil pickups. They have the coil in a tub like ferromagnetic material that is about 1mm or more thick. It needs much thicker to block audio frequency EM wave. For microwave, very thin material will do, but then you have to worry about little holes and crack of the cage as any opening comparable to the wavelength will allow EM to weak out.