Swain and Robinson-Baker finished behind the Chinese and Russians
Britain's Ben Swain and Nick Robinson-Baker took bronze in the opening Diving World Series event in Doha but Tom Daley failed to reach his final.
Daley, 14, has been struggling with a back problem and could only finish fourth in his 10m platform semi-final.
But his score of 483.35 - short of his best of 517.55 - would have been enough to get through the other semi.
Swain and Robinson-Baker scored 414.18 in the men's 3m springboard synchro to take third place.
Chinese duo Wang Feng and Qin Kai claimed gold with a score of 452.67 while silver medal to Russians Dmitry Sautin and Yuriy Kunakov (429.27).
Rebecca Gallantree, Britain's only other competitor at the meet, finished fourth in her semi-final of the women's 3m springboard and took eighth place overall.
The British squad will then travel to Changzhou, China to take part in the second leg of the series which begins on 27 March.
The squad return to England for the British leg which takes place at Ponds Forge in Sheffield on 18-19 April.