Harvard University got its wish on Wednesday when a federal judge ruled that the Trump administration had illegally cut off billions of dollars in research money.

Less clear is when or whether Harvard will actually get the money again.

The White House asserted that the university “remains ineligible for grants in the future,” a blanket declaration that appeared to clash with Wednesday’s decision, and vowed an appeal. And the judge in Boston who ruled against the administration, Allison D. Burroughs, signaled that the government could still use customary tactics to try to choke off federal funding in the future.

Although Wednesday’s ruling principally focused on Harvard’s plight, university leaders and lawyers across the country were studying it carefully into Thursday, sifting for clues about how they might, or might not, be able to counter any Trump administration campaigns against their campuses.

What they found was a muddled outlook that might do only so much to deter President Trump’s crusade of funding cuts, settlements and enormous financial demands against universities. Before this week’s ruling, the administration was putting particular pressure on Cornell, Duke, Princeton, the University of California, Los Angeles, and Northwestern — whose president said Thursday that he would resign.

“What we’re learning is that winning is not necessarily winning,” Ted Mitchell, the president of the American Council on Education, said of the Harvard decision on Thursday, adding: “Certainly, Harvard has won this battle. But the war against higher education remains in full force.”

A day earlier, Judge Burroughs was unsparing in her critiques of the administration, which she wrote had “used antisemitism as a smoke screen for a targeted, ideologically motivated assault on this country’s premier universities.”