Paula Pimentel held her only grandchild, Ben, now a year old, for the first time last week.

Two weeks after receiving her second dose of a Covid-19 vaccine, Ms. Pimentel flew from Phoenix to Boston, woke the next morning in her daughter’s apartment and cradled Ben, named after her father, in her arms. That afternoon, she took him out in his stroller and fed him. At bedtime, after she read him “Goodnight Moon,” Ben reached out to her and gave her a kiss.

“Oh my gosh. I melted,” says Ms. Pimentel, 71, who had planned to be with her daughter, Rani Wise, when Ben was born in March 2020. That trip and three subsequent planned visits were scrapped because of the pandemic.

Across the country, after a year apart, newly vaccinated grandparents are getting together with their grandchildren, celebrating missed birthdays, marveling at teenagers’ growth spurts, delivering snacks to college freshmen. Many grandparents had been delaying trips until they got the vaccines and new guidelines from the Centers for Disease Control and Prevention, which came out earlier this month.

Those who have received two doses of the Pfizer or Moderna vaccine or a single dose of Johnson & Johnson and waited two weeks can gather privately without masks with others at low risk for Covid-19, the guidelines say. More than 42% of the U.S. population 65 and older is fully vaccinated, according to the CDC.