Methods and apparatus to stabilize and recover unmanned aerial vehicles (UAVs) are disclosed. A disclosed example apparatus includes a capture line, a mast to support the capture line for contact with the UAV, and a braking stabilizer. The braking stabilizer includes a flexible stem, a body at a distal end of the stem, where the body defines first and second flexible posts, and a filament extending between the first and second posts to contact and engage a hook of the UAV.