The 26-year-old finished Sunday's final in 4:09.22, producing a strong finish to secure a place on the podium.
Great Britain's Georgia Hunter Bell took the European title in 4:07.78, while Poland's Klaudia Kazimierska finished second in 4:08.80.
The result gave Silva her first medal at a major outdoor championship and continued what has already been an impressive period in her career.
The Portuguese Athletics Federation highlighted her strong form going into Birmingham. In June, Silva ran the 1,500 metres in 3:58.74 at the Diamond League meeting in Paris, making her the second-fastest Portuguese woman ever over the distance. Only Carla Sacramento's national record of 3:57.71, set in 1998, is faster.
Silva had already given an indication that she could challenge for a medal during Saturday's qualifying round. She won her heat in 4:08.17, the fastest time recorded by any athlete during qualification.
Her success in Birmingham also continues an interesting family connection with the event.
Her father, former Portuguese middle-distance runner Rui Silva, won European silver in the 1,500 metres in Budapest in 1998 and bronze in Munich in 2002. He also won Olympic bronze over the same distance at Athens 2004.
Another Portuguese athlete, Salomé Afonso, also competed in Sunday's 1,500-metre final after qualifying from her heat on Saturday. She finished the final in 11th place.
Silva's bronze completed Portugal's medal tally at the championships.
Portugal leaves Birmingham with three medals. Pedro Pablo Pichardo won silver in the men's triple jump, while Fatoumata Diallo took bronze in the women's 400 metres hurdles, setting a new Portuguese record of 53.55 seconds. Patrícia Silva's third place in the 1,500 metres added the final medal on the last day of competition.













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