Pinch off the individual blossoms in each flowering umbel after they begin to wilt. Grasp the base of the flower between your thumb and forefinger and break it off at its base.
Cut off the entire umbel once all the flowers buds at the top finish blooming. Cut off the entire stem with shears, making the cut where the stem emerges from the foliage near the base of the plant.
Inspect the agapanthus once a week for dead or declining blooms and umbels. Deadhead as needed, by removing individual flowers or entire stalks, throughout the summer months.