Are President Trump’s tariffs a case of executive overreach? That’s the question before a little-known federal tribunal at New York, the Court of International Trade. Three judges on the court today heard arguments over whether Mr. Trump wrongly relied on a 1977 law, the International Emergency Economic Powers Act, to impose some of his levies. With other cases pending, it raises the possibility that federal courts could upend Mr. Trump’s signature trade policy.

The scrutiny in the judicial branch follows a short-lived rebellion on Capitol Hill against Mr. Trump’s levies on imports, which have roiled markets. The tumult is partly a result of the uncertainty in corporate America, amid a series of contradictory messages coming from the White House, as to what level of tariffs, if any, would be imposed. Yet efforts in Congress to strip the president of his authority unilaterally to impose tariffs have so far gone nowhere.

Mr. Trump has warmed to tariffs — or the threat of them — on trade as a tool in foreign policy negotiations, a core presidential responsibility. Yet from a constitutional viewpoint, the power to set tariffs — a tax, after all — was assigned to Congress. Tariffs were not a part of the presidential toolbox until the fallout from the disastrous Smoot-Hawley tariff of 1930. After that, the legislators ceded to the president much of their authority over tariffs.

For decades, these powers largely lay dormant, with some notable exceptions. In 1983, motorcycle maker Harley-Davidson was reeling from tough Japanese competition. President Reagan on his own imposed a punitive 49.4 percent tariff on the imports. Harley hailed the move as “courageous” and proof that “free trade must also be fair trade.” Within a few years, Harley was back on its feet and the company asked for the tariffs to be removed.

Mr. Trump, though, has deployed the tariff powers handed to him by Congress to an unprecedented degree, “taking the average effective tariff rate to around 23%, a near 10-fold increase of the rate last year,” per Harvard Business Review. Does he have the law on his side? More broadly, is such a sweeping unilateral economic démarche in line with the Framers’ constitutional conception? Those questions are now being weighed by federal judges.

In the case heard today at New York, a group of small businesses contend that the answer to both questions is: No. They reckon the 1977 law used by Mr. Trump to justify his “Liberation Day” tariffs “does not authorize the President to unilaterally issue across-the-board worldwide tariffs.” Plus, too, they argue that when Congress gave the president so much leeway over tariffs, it was “an unlawful delegation of legislative power to the executive.”

The Department of Justice points to the president’s “power to conduct foreign affairs and ensure national security through the regulation of trade.” The DOJ adds that the case is “a nonjusticiable political question,” in which judges have no power to second-guess the president’s judgment. The panel of judges on the trade court on Tuesday grappled with how to decide if Mr. Trump’s moves were justified by an “unusual and extraordinary threat.”

Judge Timothy Reif, who was nominated to the bench by Mr. Trump, wondered if there are “judicially manageable standards that the court could apply to determine whether an emergency is unusual and extraordinary.” Judge Jane Restani, nominated by Reagan, allowed as how “You know it when you see it” didn’t “work” as a standard, “so give me some words.” The lawyer asked the judges to “call a strike,” not ask “where is the strike zone.”

Next week, the trade court will hear a case brought by Oregon and 11 other Democratic states suing to block the tariffs, calling them an “unprecedented misuse of emergency powers.” Meanwhile, the constitutional watchdogs at the New Civil Liberties Alliance are suing in federal court in Florida, doubting Mr. Trump’s “unlimited authority to commandeer Congress’s power over tariffs.” If judges agree, Mr. Trump could lose his ability to use trade as a policy tool.