LEDs are actually quite tough little solid state devices being essentially Diodes even when compared to very fine tungsten filaments. During an EMP the driver circuitry may become damaged but if they fail the LEDs can be removed from the housings and 4 LEDs can be arranged in series with a 12V battery such as an SLA to produce some light. Getting light out of an incandescent bulb even if perfectly functional might be a little more tricky during an EMP as access to a working inverter may prove a little more difficult. A butane gas powered soldering iron might be worthwhile purchasing. Repairing a vacuum tungsten filament is virtually impossible at home.

The LEDs will also typically last 5-6 times that of incandescent if using a limited power setup such as a DC battery (not including the inverter losses) before the battery dies (assuming that the battery even has the load capacity to even run a 40-100 Watt incandescent).

A backup butane gas powered light source/latern would also be a worthwhile having for an EMP event.

http://www.gasproducts.co.uk/acatalog/Bullfinch_1616_Handilight_Gas_Lantern.html