When bird banders catch a bird in their nets they “sex” it by blowing on the bird to part the feathers to look for a cloacal protuberance, which would only be visible in breeding male passerines.
Some birds have spectacular courtship displays. Scientists think that Bald Eagles find a mate and stay together for life unless one mate dies. When they are courting they do incredible acrobatic flight displays. One display is called the “cartwheel display”: the pair fly very high, lock talons, and tumble/cartwheel back toward earth. They let go of each other only at the last moment to avoid crashing into the ground. Watch an aerial courtship display by Bald Eagles: