Why can my portable AM radio work inside a microwave oven while the microwaves can't get out?

A couple of reasons: The microwave oven is designed to block microwaves. Certain Longer wavelengths might be able to be transmitted right through the metal oven chamber. Second, even though 'microwaves cant get out', the oven isn't perfect, and there will always be some leakage/coupling to the outside environment. Most modern radio recievers are very sensitive, so even a tiny amount of singal 'leaking in' to the oven will be enough. Try something that operates at microwave frequencies, like a mobile phone, or a wireless camera (2.4Ghz, the same frequency that the oven operates at!). I think you'll find that in all cases leakage is enough that even these things will work fine. High quality faraday cages that provide enar perfect shielding are very expensive to manufacture, and microwave oven are designed to be cheap.