Rymer, who was diagnosed with cancer in 2009, died Wednesday in a Los Angeles hospital, said a court spokesman.
"Her passion for the law and dedication to the work of the court was inspiring," 9th Circuit Chief Judge Alex Kozinski said in a news release.
A former antitrust lawyer in Los Angeles, Rymer was appointed by President Reagan as a judge of the U.S. District Court for the Central District of California in 1983.
She quickly earned a reputation for her carefully reasoned decisions and, according to a 1986 Los Angeles Times article, was considered one of the toughest sentencing judges on the U.S. District Court in Los Angeles.
In late 1986, Rymer was on Gov. George Deukmejian's list of leading candidates to fill one of three upcoming vacancies on the California Supreme Court.
But she asked Deukmejian to remove her name from consideration, writing in a letter that "I love the work that I am doing and feel committed to my appointment to the federal bench."
Since her appointment to the District Court, Rymer was often mentioned for a 9th Circuit judgeship. She also was on a list of candidates considered for the U.S. Supreme Court before Reagan nominated Kennedy.
Elevated to the 9th Circuit Court of Appeals by President George H.W. Bush in 1989, Rymer sat on more than 800 merits panels and wrote 335 panel opinions during her 22 years on the appellate court.
"In terms of judging cases, she had a brilliant, focused mind and could cut to the heart of the matter very efficiently and quickly and always strove to do the right thing by the parties," said Judge Kim McLane Wardlaw.
Wardlaw, who sat with Rymer numerous times, described her as "a very moderate, fair-minded, opened-minded jurist."
Among the significant cases that Rymer wrote for the majority of the court was Planned Parenthood vs. American Coalition of Life Activists (2002), which held that Internet threats against doctors who performed abortions were not protected by the First 1st Amendment.
In 2008, she also wrote for the majority of the court in United States vs. Carty, which established appellate review procedures for the new advisory sentencing guidelines.
Said Judge Stephen Trott: "Not only was she a brilliant jurist and a joy to work with, what stands out with Pam was her devotion to making sure that our work got out as promptly as possible.
"Because of her experience in private practice and as a trial court judge, she was acutely aware of how important it is to resolve controversies as quickly as possible. Never once was she behind in her work during [the] entire time she sat on the court.
"She was a model for all of us in that respect."
Off the bench, Rymer was known for her playful sense of humor and the array of stuffed, ceramic and glass frogs — and other frog-related items, most of them gifts to her — that she kept in her office and home.
The collection grew out of a prank she pulled decades ago when, as an associate at the Los Angeles law firm of Lillick, McHose & Charles, she surreptitiously placed a live frog in a senior partner's desk drawer.
An only child, Rymer was born Jan. 16, 1941, in Knoxville, Tenn., and grew up in the San Francisco Bay Area.
She earned a bachelor's degree in political science from Vassar College in 1961. After graduating from Stanford Law School in 1964, she served as director of political research and analysis for Republican Sen. Barry Goldwater's unsuccessful presidential election campaign.
She launched her law career in 1965 with Rus Walton & Associates in Los Altos, Calif. She later became a partner at Lillick, McHose & Charles and co-founded her own firm, Toy & Rymer, in 1975.
Rymer remained loyal to Stanford University, including serving as a member of the school's board of trustees from 1991 to 2001.
In 2010, she received the Stanford Medal in recognition to her many years of volunteer work on behalf of the school, where two scholarship funds have been established in her name.
She had no immediate surviving family members. At her request, no services will be held.