Katty Kay and Claire Shipman hardly seem like victims of self-doubt. Between them, they have covered the Clinton White House and the fall of the Soviet Union Ms. Shipman, anchors BBC World News America Ms. Kay and learned to kiteboard at nearly 40 Ms. Kay again. And yet both say they have had to work to overcome fears of inadequacy, tendencies to defer to male colleagues and “tortured cycles of useless self-recrimination.” In “The Confidence Code,” to be published on Tuesday, they lay out a path for women to become more self-assured. In phone conversations and at a lunch date served by Sidra Forman, a Washington chef, Ms. Kay and Ms. Shipman discussed how to swat away creeping negative thoughts and what they are really thinking when they’re on television. This interview has been edited and condensed.