Confidence comes from two main sources: knowing how to answer the case and how you present yourself. Andrea & Amir have both touched upon the case aspect and indeed the more you practice the more confident you will become. But then there's the aspect of how you present yourself.
Body language is 2/3rds the communication. Sitting with your back hunched over, speaking in a low voice and not making eye contact all reflect a lack of confidence. Why is this important? Because one needs to instil confidence in the client. It is important for the client to feel that you know what you're doing and trust what you're saying. Consulting is a people job as much as it is an analytical job.
Here are a few tips to help you gain confidence. There are other ways of course, but these can help you get started:-
1. Practice walking with purpose. No swaying. No bouncing. No shuffling steps, or long awkward strides.
2. Have a firm hand shake.
3. Sit up in the interview, hands clasped in front of you. Plant your bum on the whole seat - not just the edge, and push your back against the back of the seat. This will force you to sit up with an erect spine and shoulders back. It is ok to lean in from time to time to show that you are engaged in the conversation.
4. Don't hold on to a pen or anything else - you will start fiddling with it and it will exacerbate your anxiety.
5. Make eye contact. Don't stare them down though.
6. Speak in a clear, calm and unrushed manner. Don't whisper but equally don't shout. Also don't mumble. Think before you speak - count to 5 in your head if you must.
Hope these tips help!