EMP can change chemical composition, so this is important. More on that later.

Electronics can be wrapped once or multiple times in foil and put in plastic bag, or simply put into anti ESD (metalized) protective bag. It works as a protection and can easily be done. This way you will be sure, that you've done everything to protect this thing. Layering will not provide significantly better protection than wrapping multiple times into thick layer of foil without plastic bag between layers. It's not worth the effort. Thick wrapping can dissipate thermal energy much better and thus works better. It becomes something in between sold thick metal, which is the best, and a foil.
Plastic bag or several of them after that is a must. This is a chemically sensitive device.
For small critical devices it's possible to make custom, improved in many ways box.

First of all there is no ultimate protection. Weapons are improved all the time. If it will get hit by extreme some new type EMP, you will be close to ground zero (SREMP), or radiation protection won't be adequate (SGEMP), foil can melt inside and the same can happen with every microchip in the device. The question should be how human being can survive to see it happening, which is much more complicated task. EMP protection in this case is deeper underground to protect against radiation, thicker walls, additional internal thick high permeability metal box. Resources needed for protection grow exponentially from some point.

Galvanized steel trash can should offer adequate protect against known types of EMP and mentioned standard is also based on known types of EMP. It should provide good protection. The best protection is always in the middle of box. Only one part, contact between lid and can may be improved with conductive gasket. More layers of protection make better overall protection. Big can, smaller boxes and foil is a good improved protection.

I'm not using foil at all, the box should handle EMP, but there are no critical things for survival, so situation is different. Anti ESD bags are used for some spare parts that are sensitive or have open contacts. Usually these parts come with such bags, ant it's better to keep them there or use foil. When moving with a backpack or unpacking foil, it makes lots of sound and it's a big disadvantage. For backpack or portable anti EMP box I'm using metal box with lining made from RF absorbing material and anti ESD sponge that keeps things tight so that they do not break and do not cause sounds.