Final answer:
The Executive Branch is responsible for nominating justices of the Supreme Court. The President has the power to nominate federal judges, including Supreme Court justices, and their appointment must be confirmed by the Senate.
Step-by-step explanation:
The branch of government that nominates justices of the Supreme Court is the Executive Branch. According to Article II, Section 2 of the Constitution, the President has the power to nominate federal judges, including Supreme Court justices. Once the President nominates a candidate, their appointment must be confirmed by a majority vote in the Senate.