This paper presents a simple method to boost the robustness of quadrotors in trajectory tracking. The presented method features a high-gain disturbance observer (HGDO) that provides disturbance estimates in real-time. The estimates are then used in a trajectory control law to compensate for disturbance effects. We present theoretical convergence results showing that the proposed HGDO can quickly converge to an adjustable neighborhood of actual disturbance values. We will then integrate the disturbance estimates with a typical robust trajectory controller, namely sliding mode control (SMC), and present Lyapunov stability analysis to establish the boundedness of trajectory tracking errors. However, our stability analysis can be easily extended to other Lyapunov-based controllers to develop different HGDO-based controllers with formal stability guarantees. We evaluate the proposed HGDO-based control method using both simulation and laboratory experiments in various scenarios and in the presence of external disturbances. Our results indicate that the addition of HGDO to a quadrotor trajectory controller can significantly improve the accuracy and precision of trajectory tracking in the presence of external disturbances.