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Friday afternoon last week, Jensen Huang, the chief executive of the chipmaker Nvidia, slipped into the White House to meet President Trump for the first time. There was no fanfare, and he left without a single public photo taken of the two.

Two weeks earlier, Microsoft’s chief executive, Satya Nadella, had a lengthy lunch with Mr. Trump at his Mar-a-Lago estate in Florida. They dined with little fuss and also barely made the news.

Neither executive joined his big tech contemporaries who stood ramrod behind Mr. Trump at his inauguration. Instead, the two were on entirely different continents: Mr. Nadella was traveling to the World Economic Forum in Davos, Switzerland, while Mr. Huang was wrapping up a visit to see suppliers and employees in Taiwan and China.

The absence at the inauguration of the chief executives of two of the world’s most valuable companies was perhaps the most visual sign that some companies were trying a lower-key approach as Mr. Trump returned to Washington, even as some peers took to flamboyant displays of courtship.

For companies like Microsoft and Nvidia, which unlike many of their peers haven’t angered Mr. Trump, “it is almost business as usual,” said S. Somasegar, a former Microsoft executive now at Madrona Venture Group who speaks regularly with Mr. Nadella.

While Microsoft and Nvidia share a quieter approach to Mr. Trump, their footprints in Washington are the polar opposite. Microsoft, on the cusp of its 50th anniversary and schooled by its antitrust fight more than two decades ago, is arguably tech’s savviest player on policy issues, with a strong lobbying arm and executives who have nurtured contacts in both political parties.

Nvidia, on the other hand, is a rookie in Washington. Its profile has grown rapidly in the last few years, thanks to its overwhelming control of the specialized chips that other tech companies need to build big A.I. systems.

The stakes for both companies are high. The new administration has to finalize rules about the sale of Nvidia chips and building Microsoft data centers overseas. Microsoft also has an array of other concerns, including cybersecurity, the regulation of A.I. systems and the electricity demands to power data centers. After a breakthrough development by the startup DeepSeek, Nvidia also faces a risk that the administration could further curtail sales of its chips to China.

“Everyone has to come to the table, and they will do it in different ways, because as the saying goes, if you’re not at the table, you’re on the menu,” said Kevin Madden, a senior partner at Penta Group, a global strategy firm, and a former senior strategist on Mitt Romney’s 2012 presidential campaign.

Their quieter strategies were on display around the inauguration. Brad Smith, Microsoft’s president, attended a reception for cabinet members hosted by Vice President JD Vance. A week later, Mr. Smith and Mr. Nadella went to a black-tie dinner that was hosted by the Alfalfa Club and attended by the cabinet nominees Howard Lutnick, Linda McMahon and Doug Burgum, the former governor of North Dakota and Mr. Nadella’s old mentor at Microsoft. Nvidia’s vice president of external affairs, Ned Finkle, and some of Nvidia’s policy staff also attended inauguration celebrations.

Like other tech companies, Microsoft donated $1 million to Mr. Trump’s inauguration fund, but it did so after its peers. It gave $500,000 to the inaugural fund for the first Trump administration, as well as the Biden inauguration in 2021. (Nvidia did not donate to the inaugural fund.)

When the Amazon founder Jeff Bezos and his fiancée, Lauren Sánchez, had dinner in a much anticipated trip to Mar-a-Lago in mid-December, Instagram posts documenting it made the gossip pages.

Microsoft leaders met with Mr. Trump’s staff, cabinet appointees and technology advisers in advance of Mr. Nadella, the person said. When they arrived at Mar-a-Lago, they knew Mr. Trump’s priorities and concerns.

They spoke about security and investing in infrastructure, and when Mr. Trump expressed concern about the safety of nuclear power — which is gaining popularity as a supplier of electricity for data centers — Mr. Nadella, Mr. Smith and Elon Musk, who joined the lunch, tried to assuage his fears, according to a person with knowledge of the conversation.

Nvidia’s Mr. Huang skipped Mar-a-Lago and waited nearly two weeks after the inauguration to visit the administration.

By the time he arrived in Washington this month, it had become clear that the Trump administration could be a threat to Nvidia’s business. Mr. Lutnick, a wealthy donor to Mr. Trump who had been chosen to lead the Commerce Department, told Congress during his nomination hearing days earlier that he thought the American tech companies, including Nvidia, “need to stop helping” China.

“If they’re going to compete with us, let them compete, but stop using our tools to compete with us,” he said.

The comments shattered Nvidia’s hopes that Mr. Trump might usher in a lighter regulatory environment than his predecessor. Under President Joseph R. Biden Jr., the United States curbed the sale of Nvidia chips to China and capped the sales of its A.I. chips to more than 100 other countries. The expansion and enforcement of those rules fall to the Trump administration.

During Mr. Huang’s afternoon meeting with Mr. Trump, their first ever, Mr. Huang talked about A.I. policy and semiconductors. But afterward, Mr. Trump told reporters that he couldn’t say whether he would ban more of Nvidia’s chip sales to China. He added that while “it was a good meeting,” the administration still planned to put tariffs on chips made overseas, which would cut into Nvidia’s profits because its chips are made in Taiwan.

“He’s a great gentleman,” Mr. Trump said of Mr. Huang. “He’s the biggest in the world in terms of chips.”

Mr. Finkle declined to discuss the meeting. In an interview with The New York Times, he said, “Things went well, but I can’t say much more than that.”

In the face of the White House’s pressure, Nvidia has been beefing up its Washington presence. This week, the company, which opened its first office there last year, brought on board a Republican government affairs executive, Stewart Barber, who previously worked as an adviser to Ivanka Trump, said two people familiar with Nvidia’s office who asked for anonymity to discuss personnel.

The company has applied to become a member of the Information Technology Industry Council, a policy group that represents most of the leading tech companies. It has also hired American Global Strategies, a geopolitical advisory group led by Robert C. O’Brien, who served as White House national security adviser for two years under Mr. Trump.

Nvidia’s belated expansion in Washington can also be attributed to a recognition that its newfound prominence demanded it become more engaged. In a little over a year, Nvidia’s market value has ballooned by $2 trillion, making it one of the world’s three most valuable public companies, with Microsoft and Apple.

“This really shows their maturation and recognition that having a presence in Washington matters,” said Dean Garfield, a former senior vice president of policy at Netflix, who led the Information Technology Industry Council from 2009 to 2018. “Hopefully, it’s one of multiple steps they take.”