In her dining room. On the telephone.
"I'm going to replicate the process as much as possible," said Blatt, though the only people who will see her Monday are a son who's in charge of the dog, a daughter who will intercept anyone who approaches the house, a colleague at the table and Blatt's husband David, acting as timekeeper.
It is unclear exactly where the nine justices will be - other than apart - as they begin two weeks of oral arguments unlike any in the court's 230-year history.
The coronavirus pandemic has forced changes at the Supreme Court that decades of nagging from the legal academy and threats from congressional critics failed to achieve.
Not only will the arguments be conducted by telephone - a Zoom meeting might be a bridge too far for the videophobic justices - the world for the first time will be able to listen in live, as the cases are argued.
Anyone who finds that less than remarkable in the 21st century has likely never noticed that bronze tortoises are an architectural feature at the Supreme Court, where counsellors still receive a commemorative quill pen.
The justices are making adjustments for the arguments, including asking questions one-by-one by seniority rather than the usual free-for-all, and the lawyers are as well.
At the Justice Department, whose attorneys will take part in nine of the 10 scheduled arguments, the pleas will be made to a speakerphone in the solicitor general's conference room. They will still be wearing morning coats, the formal, traditional dress for government lawyers who argue before the court.
Lawyers on the West Coast, including one making his first Supreme Court argument, will rise before dawn to await the justices' call.
Blatt will be arguing her 40th Supreme Court case, more than any other woman, and was selected by the court for the first argument in its experiment. "What could I say?" she recalled. " 'Of course. Happy to. Honored to.' "
Like most repeat Supreme Court practitioners, her preparation is intense, with moot courts in which lawyers try to ask the toughest questions, and rounds of brainstorming sessions with colleagues at the Washington firm of Williams & Connolly, where she and David are partners.
But if she is reverent about the court, she is equally irreverent about everything else, and mentions another part of her personal argument regimen.
"I did the root touch-up and straightened my hair, at home," she said in a telephone interview. "The only thing I did not do is get my Botox replenished. It's just not possible, so I'm doing my argument in wrinkles."
Blatt, who will be representing Booking.com in an otherwise nondescript trademark dispute, says she is fiercely competitive, and has a won-loss record of 36-2-1. (The justices decide one of her cases last term.)
She is not a student of the philosophy that oral arguments are a conversation between the justices and the advocates.
"An 'argument' is just that: It involves combative communication and intense verbal jousting," she wrote in a recent law review article. "You either win or lose. Or, as I like to frame every case I argue, someone is going to die, and I don't want it to be me."
In her last outing at the court in January, Blatt felt her male opponent had been condescending and unnecessarily denigrating of the legal case she had just presented.
When Chief Justice John Roberts told her she had five minutes for rebuttal, Blatt replied, "You may want to cut me off."
She added: "I don't know what to say. I didn't go to a fancy law school, but I'm very confident in my representation of the case law." Blatt, who received her law degree summa cum laude from the University of Texas, won the case in a 9-to-0 vote.
Blatt's adversary in the upcoming case, Justice Department lawyer Erica Ross, declined to be interviewed, as is customary for government lawyers.
Their trademark argument might not set ratings records for C-Span, which plans to broadcast the court's proceedings. But on May 12, the court is scheduled to take up President Donald Trump's efforts to shield his financial records from congressional committees and a New York prosecutor.
While many lawyers see an argument at the Supreme Court as a career pinnacle, its impact on the outcome of the case is not particularly prized, at least by the justices.
They have said in the past that arguments are important, but likely change the outcome in a few cases each term. Justice Stephen Breyer, for instance, has said he has opposed televising the arguments because he thinks it would give the public a distorted view of their relevance.
More important is what comes before the argument, he said: the facts of the case, the lower court's decision, the court's precedents, the briefs filed by opposing counsel arguing the law and from amicus groups alerting the justices to the consequences of their decisions.
There is no requirement for oral arguments, and the court decides a few cases each term on the briefs alone. It routinely decides emergency requests without arguments, such as its recent intervention into absentee voting in Wisconsin's primary.
But arguments are the only time the justices discuss cases in public before deciding them. And they acknowledge that they give them a chance to challenge the parties' legal arguments and test the consequences of writing an opinion a certain way.
Oral arguments are especially dear to some members of the court. Roberts was a widely lauded Supreme Court advocate before he became a judge. Ruth Bader Ginsburg made her mark arguing gender discrimination cases before the then-all-male court. Elena Kagan was President Barack Obama's solicitor general, representing the administration at the court.
Stanford law professor Jeffrey Fisher said oral arguments are an advocate's last chance. "I see it as your opportunity to try to get through to them if you haven't gotten through to them already," he said.
But he said arguing by telephone will be difficult. "I cannot imagine giving argument without seeing their faces, without seeing their expressions and all the rest," he said. "I just think that's going to make the argument so much harder."
Fisher said he already faced that choice once. The night before an argument, he broke his glasses and had no way to get them repaired before heading to the court.
He had to decide whether to wear a spare pair of contact lenses, which would correct his nearsightedness and allow him to see the justices, or go without, which would allow him to see his notes. He wore the contacts.
Fisher on May 11 is scheduled to represent two teachers in a case about whether the First Amendment protects religious schools against anti-discrimination laws. He expects to leave his Menlo Park, California, home before 6 a.m.
"My plan is to go sit in a conference room, lock the door and spread my stuff out," he said.
Coincidentally, his opponent in the case is Eric Rassback, another Bay Area lawyer who is vice president and senior counsel at the Becket Fund for Religious Liberty.
Rassback said he will put on a suit and drive to a law firm conference room to deliver what will be his first argument before the Supreme Court.
Does he fill a little cheated to be missing out on the grandeur of the Supreme Court courtroom?
"No!' he said brightly. "I get to be a footnote in history."