Christians and Atheists: How should I deal with anxiety in dating?

I am 32 and at one point was very good with women, but in the last few years have become extremely sensitive and apprehensive. I have no trouble talking to women or getting a date, but once I really like her, I completely crumble. I lack confidence, cannot be myself, even get depressed and overwhelmed with anxiety. So my follow up after the first or second date is really weak and I have soon lost her.

I know how to socialize and "what to do" but how can I manage my anxiety or not lose focus, stop over analyzing, worrying, etc?

Do you have specific things you do? I'd like to be more confident and centered for the long haul...