Many U.S. graduations are curtailed again, but some commencements will go on without guests.

Yale plans to hold a version of in-person graduation for the class of 2021 in May — with no guests allowed. Harvard is not even calling its commencement a “commencement.” It plans to hold virtual degree-granting ceremonies and, for the second year in a row, will postpone traditional festivities.

The universities of South Florida, Southern California, Pennsylvania, North Carolina at Chapel Hill, Vanderbilt, Rochester and Kentucky, among others, are holding in-person commencements, but with differing rules about guests.

So it goes in this second graduation season of the pandemic. Day by day, another university announces commencement plans, and given the uncertainty created by the coronavirus, the decisions are breaking in opposite ways.

Prairie View A&M in Texas plans to hold live commencements, even as, somewhat surreally, the president of the college, Ruth Simmons, will be delivering the principal address at Harvard’s virtual commencement.

In the United States, reported coronavirus cases and deaths have fallen significantly after a post-holiday surge, according to a New York Times database. Vaccinations have also picked up, averaging about 2.5 million shots a day, as eligibility expands in several states.

Experts warn, however, that dangerous variants could lead to a spike in cases and states that lift restrictions could be acting prematurely.

Many universities are stipulating that in order to participate in graduation, students must have tested negative for the coronavirus before the ceremony and have a good record of adhering to campus policies created to guard against infection.

Peter Salovey, the president of Yale, said in a statement this month that the university would be recognizing graduation by holding in-person gatherings “on or around May 24, if public health conditions permit.” Students studying both on campus and remotely are invited, but not their guests. Mr. Salovey said Yale was excluding families because it seemed unlikely that everybody would be vaccinated by graduation day.

Harvard was one of the first universities to evacuate its campus in mid-March last year, and it is still in caution mode. In an email to students on Feb. 26, its president, Lawrence Bacow, said that postponing live commencement for two years running was “deeply disappointing, but public health and safety must continue to take precedence.”

Like other universities, though, Harvard promised to bring the classes of 2020 and 2021 back to celebrate at some future date.

Some universities plan to hold their commencements in outdoor stadiums. Notre Dame, which was aggressive about bringing students back to campus last fall, is planning to accommodate all 3,000 graduates and a limited number of guests in its 79,000-seat stadium. Health officials have authorized the use of up to 20 percent of the seating.

The University of Southern California will hold in-person ceremonies for the classes of 2021 and 2020 in May. The ceremonies will take place at the Los Angeles Memorial Coliseum and graduates will be allowed to invite two guests, although they must be California residents.

Northeastern University in Boston will host five commencement ceremonies in Fenway Park in May. Officials are aiming to allow each graduate to invite one guest, though they are still evaluating total capacity with physical distancing.

The University of South Florida in Tampa said this month that its commencement would take place at nearby Tropicana Field, which can hold about 40,000 people. The university set a tentative date of May 7 to 9. Students will be allowed to bring two guests and must register in advance.

Some schools are holding ceremonies without guests, in what will be largely empty stadiums.

The University of Wisconsin-Madison will hold in-person ceremonies in its Camp Randall Stadium, which can hold about 80,000 people. The university will hold two ceremonies on May 8, but graduates cannot bring guests.

Princeton plans to hold an outdoor commencement at its stadium for students who have taken part in the testing program and who live on or near campus. It is also considering extending the invitation to students learning virtually.

Princeton is still deciding whether to allow guests at its in-person ceremony, and summed up the uncertainty this way: “Families are encouraged not to make nonrefundable travel arrangements.”

Some universities are moving forward with entirely virtual commencements. Columbia is planning a virtual ceremony, but has held out some hope of smaller outdoor events. New York University and Stanford University have also announced plans to hold virtual celebrations.