joyce, i totally understand about feeling under pressure to perform in face of such a great supervisor! you want to impress them, make a good first and subsequent impressions, you want to get the most out of them, you want them to think you are good. you might be worried that they will discover you for a fraud.
my sup is famous and great, too. i found that the way i manage is that i simply stopped worrying about the impression i make on her - instead i always listen very carefully to what she says. there is so much to learn from her! so our meetings are less about arguing my point or such, but more about: i throw out an idea and then observe what she does with it. and learn from that. this works for me. maybe you could re-define the supervisory meetings in your head, from an occasion where you need to prove yourself, to an occasion where you have the opportunity to learn from these smart people?