Ramirez told the magazine she was on the floor, drunk at a Yale party when the alleged incident took place.
This isn't the first time allegations have come up during a Supreme Court confirmation hearing.
"There's a chance that this could be one of the single most unfair, unjust things to happen to a candidate for anything, " Trump said.
It is something, she said, that was not surprising to hear given the culture of drinking and partying, but she remembers being struck by the "gravity" of what was being talked about. "I knew that's not what I wanted, even in that state of mind".
The New Yorker on Sunday published an accusation from a second woman, who said Kavanaugh exposed himself and forced her to touch his genitals while both were at Yale.
'I was embarrassed and ashamed and humiliated, ' Ramirez recalled. Ford had written a letter to a California lawmaker about the claim months ago that was passed to Feinstein, but had requested anonymity, and Feinstein said she was trying to honor that. She later revealed that she thought he might inadvertently kill her during the alleged incident.
The New Yorker said the allegation came to the attention of Democratic senators through a civil rights lawyer.
The journalists behind the piece, Ronan Farrow and Jane Mayer, say they contacted dozens of classmates to try and corroborate Ms Ramirez's account.
Tropical Storm Kirk forms off African coast
The storm is expected to reach the Lesser Antilles still at tropical storm strength by Friday, though some weakening is expected. They have maximum sustained winds of 25 mph and are about 350 miles east-northeast of the Windward Islands.
A survey of more than 800 likely Texas voters showed that most believe the U.S. Senate should confirm Judge Brett Kavanaugh to the U.S. Supreme Court, according to findings released by Quinnipiac University.
'This alleged event from 35 years ago did not happen.
"This is a smear, plain and simple".
In his statement Sunday, Kavanaugh said he is looking forward "to testifying on Thursday about the truth, and defending my good name - and the reputation for character and integrity I have spent a lifetime building-against these last-minute allegations".
A White House spokeswoman says the administration stands by the nominee, labelling the allegation "the latest in coordinated smear campaign by the Democrats created to tear a good man down".
Miranda said staff from the Senate Judiciary Committee had reached out to her, something she was not expecting.
Ford's attorneys and Senate Judiciary Committee aides held a conference call later Thursday, which a source told CNN lasted an hour.
Kavanaugh has firmly denied Dr. Ford's claim that he drunkenly assaulted her at a house party in the 1980s.
Senator Kirsten Gillibrand, a New York Democrat, said at the event: "Someone who is lying does not ask the FBI to investigate their claims".
Kavanaugh and the other individual, Mark Judge, then put on loud music before Kavanaugh began groping and attempting to undress her. Kavanaugh, Ford said, put his hand over her mouth to silence her after she yelled, prompting her to fear for her life.