In 1957/58, Cardoso won the zonal tournament in Baguio City, thus qualifying him for the 1958 Portorož Interzonal tournament, in which he finished 19th (Mikhail Tal won). In this tournament he scored an upset win over David Bronstein in the final round, thereby denying him a place in the 1959 Candidates' Tournament. He was Philippine Champion in 1958 and 1963. He took second place at Christchurch 1967 (New Zealand championship, won by Yuri Averbakh). In 1974, he tied for first through fourth place in Casablanca. In 1974, he took 14th in Manila (Evgeni Vasiukov won). In 1975, he tied for 13-14th in Orense. In 1975, he took 10th in Las Palmas (Ruy Lopez Memorial tournament, won by Ljubomir Ljubojević).