To determine if something will function as a faraday cage, I suppose one could start with an understanding of RF currents. I have been using radio for a while so here is my take on it. As some already stated, there are different frequency components to an EMP attack. Lets start with higher frequencies and
skin effect. Eddy currents in the metal force the majority of the current to flow within the first few mm of the material. If the metal used in your faraday cage is thin with respect to skin depth, the currents on the outside will be seen on the inside. This issue must be considered for all frequencies you encounter and becomes more of an issue for lower frequencies.
The next thing we must consider are the gaps and seams that are not sealed off. This issue is also one of frequency. In microwave ovens, that door mesh is effective at blocking most of the radiation for two reasons, one, for a metal surface to reflect RF current, ideally, it should be large with respect to a wavelength (like hams bouncing UHF signals off aircraft), which the mesh in the door is, and two, the openings are smaller than 1/20 of a wavelength meaning they cannot act as a
slot antenna on that frequency absorbing and re-radiating the energy. Imagine taking a piece of sheet metal and cutting out a 1/2 wave dipole antenna. The piece you removed can be used as an antenna, but in the same way, so can the plate with the slot. The only differences are the method of feeding (for radio) and polarization (of the signal it transmits and receives). Any gaps can act like a slot antenna, absorb and re-radiate, and allow RF current inside a faraday cage. However, in this situation, what is allowed through are the frequencies the slots or holes resonate on and their higher harmonics (which only allows a portion of the spectrum through).
To seal these gaps up does not necessarily require major effort. Some metal foil tape will do just fine. Some might disagree because the sticky side is not making electrical contact, but to that I'd argue capacitive reactance. Those two metal surfaces "not in contact" are so close that the capacitor formed is essentially a dead short to RF signals higher than a few MHz (which is how those cellular antennas that stick to your window transfer signal).
The lower frequencies that can pass through the metal will not be much of a concern either as the conductors in the devices you store inside it will be an insignificant fraction of a wavelength and therefore not couple the energy. most electronics are damaged by electromagnetic pulses because the device is powered on when the pulse hits. The pulse induces a tiny current on the MOSFET and JFET gates (solid state switches) turning them all on at the same time. If a device with power has all of its thousands of semiconductor switches turn on at the same time, the smoke is surely to be let out. I doubt you will store your devices turned on, and again, due to the small size making them inefficient antennas, not enough energy will couple to fry anything if the battery is not connected.
At the end of the day, you could just store your smaller stuff under 10 feet of water in a sealed plastic pipe. As long as the device is not connected to anything that makes an effective antenna on VLF (which is thousands of feet), it will be fine. The water will block the rest.