This is a complicated question, but I'll do my best to tackle it. Confidence comes in many shapes and forms, and it does not necessarily have to translate into pride. As a rule of thumb, I try to inspire confidence in my interactions with others, while simultaneously being humble towards the person I am facing.
One strategy I use to manage and achieve this balance is visualizations. The easiest way to do this is to close your eyes a couple of hours before an interview and imagine yourself going through the actual interview. What would you say at a difficult question? What would your posture and reaction look like? Great, now visualize it in as much detail as you can. What about a question about your accomplishments? If you do this thoroughly and visualize what your ideal response and reaction would be, then I can attest that the actual interview will come pretty close to that.