The cage on your microwave works (probably). Does your hand get hot if you hold it nearby? If not, you have nothing to worry about. The cage only needs to cut down the power getting out by a factor of 1000 or so, and then it wouldn’t pose a threat to you.
With a cell phone, the radiation is in the same frequency range, but you’re dealing with a dramatically more sophisticated beast. Cell phones have variable amplifiers, error-correcting codes, and other engineering tricks that can handle a huge dynamic range of signal strengths, ranging from the enormous signal you’d get if you were standing under a cell tower all the way to the minuscule signal you’d get out in the wilderness. Remember, the power of the radiated signal from a tower decreases as $1/r^2$, so your phone has to be able to measure small signals to be useful. If you have a decent cell signal at your house to begin with, it doesn’t matter if you put the phone in a cage that drops the signal by a factor of 1000. That’s the difference between being away from a cell tower by 50 meters versus a mile: the phone can handle it.