The Nationals announced the moves Saturday before their game against the Marlins.
Broderick was obtained in the Rule 5 draft from St. Louis in December and was 0-1 with a 6.57 ERA in 11 appearances. He was the loser in Friday's 6-5, 11-inning defeat to Florida.
Kimball made 12 appearances for Syracuse, and didn't allow a run in 13 2/3 innings. He's 1-0 with five saves. The 25-year-old has never pitched in the major leagues.