what is the best way to cook fillet steaks?
i normally cook them in a grill pan on a high heat but can't seem to cook them to my liking which is well done without it being burnt on the outside. Any suggestions?

If the steak is thick, then you can always butterfly it and cook it quicker

Hello steak and chips
If the steak is good enough - you'd eat it raw!
Just make sure the heat is high enough to seal the steak on both sides properly then turn the heat down a little so that the smoke alarms don't go off and then cook your steak for a little longer for them to be well done! Make sure that the extractor fans are on full blast - et voila!

How about sealing it very briefly in a pan, then popping in the oven, testing every so often, until it is done the way you like. The ouside should be less likely to burn this way.