Why did my attempt at pan-searing beef filets fail miserably?
Butter is a very bad choice for frying at high heat, as it burns extremely easily. Cast iron is the ideal pan material though, so you are halfway there. 


Take a flavourless oil like sunflower and brush it
directly on the steaks - don't put the oil in the pan. 
Preheat the pan until it is ridiculously hot.
Preheat the oven if that's the
method you're going to use
Season the steaks generously with salt and
pepper
Sear the steaks and cook in the oven until desired level of
doneness is reached.
Rest the steak on a wire rack (or failing that, a plate) for 5 minutes so it doesn't leak juice all over the plate.


Personally I would omit the oven stage and just cook the steaks in the pan, turning frequently. Add a knob of butter near the end and baste it over the steaks with a spoon.

A probe thermometer is a great investment to make if you plan on cooking meat properly. You cannot rely on rules of thumb like pressing the steak or just timing it. There is a good chart here for the temperatures at each level of 'doneness'.