Judicial reviews have been brought by protest groups claiming failures in consultation and in assessing the high-speed link’s environmental impact.
The government has said it “struck the right balance” between people’s concerns and the national interest, reports The BBC.
HS2’s first phase, linking London and Birmingham, aims to be running by 2025.
The second phase of the £33bn project, north from Birmingham in a Y-shaped extension to Manchester and Leeds, could be operational by about 2032-33.
BBC transport correspondent Richard Westcott said: “It is incredibly unlikely that today’s judgement will stop the project.
“Instead, campaigners want to delay it to death, picking holes until the government has neither the time, nor the money to see it through.”
Five judicial reviews have been brought by four protest groups, including several councils and a golf club, that are among more than 70 groups opposed to HS2.
The objections being brought to court also include the claim that the government failed to adequately assess alternatives to the scheme.
The government argues that cutting rail journey times and overcrowding will bring “jobs, growth and prosperity”.
