You wouldn't be human if you didn't feel at least a twinge of nerves when interacting with important people.
We're social beings, designed to influence and be influenced, so of course you're going to notice and react to another person's success, status, or power. There's no need to tie yourself up in knots, however.
1. Name the Problem
Whether you call it anxiety, discomfort, intimidation, or something else, what's eating at you is fear. This feeling hijacks your rational thought processes, and it's crucial to ask yourself what, exactly , you're afraid of if you want to get over it.
The underlying cause of your fear will be unique to you and may vary from one situation to another. General anxiety at the thought of interacting with highly successful people may be due to your perceived inadequacy. Or maybe you were embarrassed years ago by someone powerful, so now you're afraid that situation will replay itself in your professional life.
Those fears have nothing to do with the people you're afraid of--they're about you.
On the other hand, you may periodically have to interact with a powerful person who really is a jerk, and that can certainly ratchet your fear closer to "zombie-attack" level. But even then, it's important to be realistic, which brings me to my next point.
2. Replace Hyperbole With Fact
Few people operate from a purely rational and factual mindset day in and day out. Instead, we allow our imaginations to run wild.
It looks like this: I once had a new supervisor who physically resembled a previous, difficult boss. I avoided my new manager for a while because of this. Had I not been acting irrationally though, I'd have realized physical similarity doesn't equate to matching personalities. I wouldn't have made any assumptions about the new supervisor and instead would've given her a fair chance.
When you catch your imagination running away, stop, and simply state what's factual. Let's say you've got a big luncheon that will include some bigwigs and you feel your heart start to pound. Take note of this, inhale deeply, and say to yourself, "Danny Jones is successful and socially savvy. I feel awkward next to him, and I'm afraid I'll look dumb."
3. Prepare and Practice
Once you've been honest with yourself about what's driving your fear, you can take action to reduce it, starting with being prepared. Granted, you won't always have the chance to prep for a meeting with a VIP, but often you will.
The more ready you are before the interaction, the more confident you'll be. This may not completely nix your nerves, but that's OK--a touch of anxiety can help you perform under pressure.
The idea is to reduce or prevent crippling fear. Think back to the example above. Now that you've identified what drives your fear, you might think to yourself, "I'll think ahead about some small talk I can engage in if we bump into each other. I'll even practice it out loud a few times. Then I'll feel more comfortable if we should happen to run into each other." (For your reference:48 small talk starters you can use in these situations.)
Now instead of worrying about what to say if you bump into Mr. Jones, you're armed with some ideas you can adapt and pull from as needed. And like everything in life, the more you interact with successful people, the more comfortable you'll be.
4. Mind Your Body Language
Most communication is non-verbal, and that includes the way we communicate with ourselves. If you walk around with slightly hunched shoulders and downcast eyes, not only do you appear unsure of yourself to the rest of the world, but you also communicate that uncertainty to yourself.
If you want to feel better when interacting with others, you need to project calm confidence. Stand up straight. Make eye contact. Use a firm handshake. Hold your body still--not stiff, but not fidgety, either--maintaining calm, restrained hand and arm movements while speaking.
Think consciously about projecting confidence as you go about your day. (And if you're looking for a quick tip on how to make that easier, read this.) It's far easier to practice in the relatively non-threatening environment of your family, peers, local coffee shop baristas, and so on, than to automatically make these adjustments during the interactions with someone you find intimidating. In time, though, the idea is that you'll generally demonstrate poise--no matter who you're speaking with.
So, let go of your misconceptions, own your own worth, and treat powerful people like people. As Muse writer Lily Herman puts it, "Important or famous people shouldn't be treated any differently."
Embracing this way of thinking will allow you to talk as two equals, and that's when the conversation can really take off.