Echolocating bats face the challenge of coordinating flight kinematics with the production of echolocation signals used to guide navigation. Previous studies of bat flight have focused on kinematics of fruit and nectar-feeding bats, often in wind tunnels with limited maneuvering, and without analysis of echolocation behavior. In this study, we engaged insectivorous big brown bats in a task requiring simultaneous turning and climbing flight, and used synchronized high-speed motion-tracking cameras and audio recordings to quantify the animals' coordination of wing kinematics and echolocation. Bats varied flight speed, turn rate, climb rate and wingbeat rate as they navigated around obstacles, and they adapted their sonar signals in patterning, duration and frequency in relation to the timing of flight maneuvers. We found that bats timed the emission of sonar calls with the upstroke phase of the wingbeat cycle in straight flight, and that this relationship changed when bats turned to navigate obstacles. We also characterized the unsteadiness of climbing and turning flight, as well as the relationship between speed and kinematic parameters. Adaptations in the bats' echolocation call frequency suggest changes in beam width and sonar field of view in relation to obstacles and flight behavior. By characterizing flight and sonar behaviors in an insectivorous bat species, we find evidence of exquisitely tight coordination of sensory and motor systems for obstacle navigation and insect capture.