Although theoretical work on optimal migration has been largely restricted to birds, relevant free-flight data are now becoming available for migratory insects. Here we report, for the first time in passion-vine butterflies, that Heliconius sara migrates directionally. To test optimal migration models for insects, we quantified the aerodynamic power curve for free-flying H. sara as they migrated across the Panama Canal. Using synchronized stereo-images from high-speed video cameras, we reconstructed three-dimensional flight kinematics of H. sara migrating naturally across the Panama Canal. We also reconstructed flight kinematics from a single-camera view of butterflies flying through a flight tunnel. We calculated the power requirements for flight for H. sara over a range of flight velocities. The relationship between aerodynamic power and velocity was "J"-shaped across the measured velocities with a minimum power velocity of 0.9 m/s and a maximum range velocity of 2.25 m/s. Migrating H. sara did not compensate for crosswind drift. Changes in airspeed with tailwind drift were consistent with the null hypothesis that H. sara did not compensate for tailwind drift, but they were also not significantly different from those predicted to maximize the migratory range of the insects.