Just do these three things, 1) Be honest, 1) Smile at them, 3) practice meeting them in your mind.
Be honest, when you meet them consider saying something like this
Hi, I've been really excited and kind of nervous to meet you. I think your daughter is an amazing person.
Telling them your excited to meet them (which is probably part of what is making you nervous) is flattering and will make them feel good. Telling them that your nervous will explain any shy/awkward behavior on your part. Also more importantly telling the truth about how you feel will free you up inside to be more relaxed.
And of course telling them you think their daughter is amazing is a compliment to their parenting. which will make them like you and more forgiving of any odd behavior.
Smile at them, smiling will give you more positive emotions and more positive emotions to most people who see your smile. see here
practice meeting them in your mind I did some performance in high school and I learned that practicing things in your mind is actually really useful. Just practice the perfect 1 minute first impression every morning till you meet them. practicing in your mind will convince your brain that you can pull this off.
-Bring a small gift that they will like, (ask your partners input). Even something like cookies will be well received.
-Deep slow breathing will relax you. I once had a therapist tell me that "deep breathing is the cheapest anti anxiety medicine." While not a miracle pill (or a pill at all :) ) it does help you relax From now till you meet them. Every time you feel nervous just breath deep and slow for a few minutes. Doing this sends a message to your brain saying something to the effect of, "It's ok, calm down."
-remember you had enough Charisma to catch your partner, in the long run her parents will probably see your same wonderful traits that your partner did.
You can do this! best of luck!