I honestly believe that having your clients feel comfortable around you and your camera all starts before you even take their photos. If your first time meeting them is at their photoshoot they're going to be nervous and shy because they don't know you and there's not always a lot you can do to fix that. Getting to know my clients prior to the shoot is some of the most important time I spend as a photographer. I feel that in order to capture clients naturally they need to feel comfortable and trust me. They should feel like they already know me.
That's why I do a consult with all my clients before a photoshoot, so we can get to know each other. That time is invaluable to taking better photos later. During the consult we really focus on them, and talking about their story and who they are.