I recently asked a woman "Didn't they teach you proper grammar in school?" because she started a sentence with "me" instead of naming the other person first as proper etiquette would have it.
I remember the teacher having the whole class using a sentence with "(friend's name) and I..." instead of "Me and (friend's name)..."
Yes, yes, I've read about that kind of thing before. Proper etiquette says that you should still put the other person first, so in the example you've given above it would be "The company gave Steve and me an award."