Meeting the parents?

Hey there people! I've just had this thing on my mind for a little while, and I'm not too sure about it.

I've been going out with this girl just over two months now, and everything is going really well (my first relationship so I don't really have anything else to compare it too but anyway). I've recently invited this girl over for dinner to meet my parents, but I'm a little anxious about it; considering it's the first time I've brought a girl over. She is also a little worried/scared because she thinks that they will 'grill' her (which is probably what is going to happen in the end).

It seems like a stupid/open ended question, and I'm sorry for that, but is there anyway to make things go smoothly and/or for us both to stop worrying about it?

Any advice would be nice, thank you!