January 27, 2003 12:00 PM

After the cameras stopped rolling during a rowboat scene on the New Zealand set of Ted and Sylvia Jan. 8, Gwyneth Paltrow‘s costar Daniel Craig jumped out, and her new boyfriend, Coldplay singer Chris Martin, hopped in. The quick cuddle “was very romantic,” says a witness, who adds that Martin would offer Paltrow bottled water and hugs between takes. “They were completely alone and just enjoying each other’s company.”

That sort of support is probably especially welcome to Paltrow, whose father, St. Elsewhere producer Bruce, died in October. Even before that, Paltrow, 30, said few boyfriends could measure up: “It’s hard for me, because my father was so fantastic,” she told reporters in September. “I’m totally a daddy’s girl.”

These days, she’s also Chris’s girl. The pair met at a Coldplay show last summer. Invited backstage, she chatted with Martin, 25, and gave him her phone number. They’ve since turned up together in Martin’s hometown of Exeter, England, to see a play starring his 11-year-old sister; dined with her mother, Blythe Danner, at Sting’s English country home in December; and spent Christmas with the Martins back in Exeter. Said Paltrow: “He is a sweetie.”

And a change from her previous high profile heartthrobs. An honors graduate from London’s University College, Martin confessed to Britain’s The Sun earlier this year, “I haven’t been out with a lot of girls.” Paltrow doesn’t seem to mind. “He’s just a genuine guy,” says Bob Palmer, a longtime acquaintance of the Martin family. “She deserves somebody nice, and she’s found a nice guy.”

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