Duncan (14) was second in the 13-16 85cc class and Meikle (12) was second in both the 11-12 85cc and 12-16 150cc classes.
Duncan (Yamaha) was hoping to repeat her recent win at the North Island championships and dethrone reigning national champion Micah McGoldrick, of Rangiora, at the Bartlett's Creek track.
She stayed on McGoldrick's wheel and won one of the five races, with McGoldrick clearing out to win another title.
Meikle (Honda) faced a demanding weekend, with five races in each of his events.
He had a win, two seconds and two fifths in 150cc racing, suffering two falls while leading races.
Temuka's Cody Scott won the class.
Meikle followed up with a win in the final 85cc race, placing second overall behind Hamilton's Josiah Natzke.
Other Otago riders to feature at the championships were Riley McPherson (sixth in 11-12 85cc), Sam Cuthbertson (seventh in 11-12 85cc) and Madison Latta (ninth in 8-10 85cc).
Otago rider Campbell King did not compete as he suffered concussion a week before the event.
Nearly 300 of New Zealand's best young riders competed at the championships.
A highlight was the effort of Mangakino's Kayne Lamont (16), who claimed a rare double by winning both the 15-16 125cc and 14-16 250cc classes.
Lamont now prepares for another tilt at the world junior motocross championships in France in August.
