I imagine compass swinging is a thing of the past with today's sophisticated Heading Instruments,
Nope - they still need to be done. The twin turboprops belonging to the airline I used to work for would be taken off line every so often to have a compass swing carried out - if it wasn't done before expiry of the last one (once a year maybe? can't remember) the aircraft would be restricted to flight in Day VMC only. One particular port in the network (a line maintenance base) had no suitable spot for compass swings so when an aircraft on on occasion ran out of compass swing currency at that port we had to wait a week before the weather improved enough to get it to another maintenance base to have the swing carried out. Quite frustrating!
Can't imagine how you'd compass swing a 747, but even those behemouths have standby magnetic compasses so it'd need to be done somehow...
Adam