I would think that a gallon aluminum paint bucket in the microwave would be just the ticket. Seal it down with a hammer and use crumpled baggies around the cell phones to keep them away from the walls of the paint can.
Most paint cans have a plastic coating on the inside and that might contribute to the protection.
I've read many opposing views about the expected strength of any EMP attack. My conclusion is that almost any effort to protect your devices is far better than leaving them exposed.
In reality, what are you going to protect? I'm not going to protect my cell phone, since I have it with me all the time; nor my daily use laptop. I do however protect my external hd for backups, hand held radios, emergency radio, retired laptop with misc info, battery charger, etc. Another consideration: what will be useful after a major EMP attack or CME. Will cell phone towers still work, or will there be local access to the internet?
A PC/laptop/Ipad filled with useful information, emergency radios, two-way radios, medical appliances, means of charging batteries, and such, will be of far more importance than a dead cell phone or inability to get to your cloud storage or social network.
I keep the above in a metal gun safe. Given enough warning (i.e., expected attack or huge CME), I probably would toss everything else that I could into the safe. But on a daily basis, practicality is a major consideration. If there are medical appliances you can't personally do without, I'd buy duplicates and keep those protected. If you require refrigerated medicines, I'd put a small DC powered refrigerator, with enough solar electrical generation to keep it going, in protective storage, and I would keep as many days of medication on hand as possible.
IIRC, the book "One Second After" presents a good picture of what those on insulin face under these circumstances. It also gives some idea of what life after a major EMP attack would be like - not good.