You'll have to cut your access to your power supply and go on generator (anything outside the faraday cage risks frying anything electrical inside), you'd also have to disconnect any groundings to pipework. Long runs of copper will be inducted during a huge flare, so the ground/earthing connections can at best knock off all your breakers and your generator, but at worse can surge from ground->neutral (frequently connected as a double safety) and fry things that way (note: I only heard of this happen from a lightning strike, but we're talking end-of-civilization-solar-flare here so it's worth note).
If you need internet ensure it's connected outside your faraday cage, run the Ethernet through a surge protector (with the modem or other devices power supply, which is essentially just for kicks at this point) and run the Ethernet inside the cage and connect it to a wireless router powered from outside. Connect all computers via wireless and your systems will be safe.
However, if everyone elses shit dies, your screwed as it is. You'll be one of the only people trying to connect to HN.