A few days before the inauguration, no one knew who would actually take the oath of office as president of the United States. There were cries of fraud and chicanery as a divided, surly nation continued to debate the winner of the election many weeks after the ballots had been cast.

The election of 1876 was the most disputed in American history and in some ways one of the most consequential. As Congress convenes on Wednesday to formalize President-elect Joseph R. Biden Jr.’s victory and dispense with Republican objections, many on Capitol Hill and beyond have been looking to the showdown nearly a century and a half ago for clues on how to resolve the latest clash for power.

The players in that drama have faded into obscurity. Few today remember the story of Rutherford B. Hayes, the Republican who ultimately prevailed and served four years as a tainted president. Fewer still can name his Democratic opponent, Samuel Tilden, who lost the White House despite garnering more votes. But the system that will govern Wednesday’s debate was fashioned from that episode, and the standards that were set then are now cited as arguments in the effort to overturn President Trump’s defeat.

Allies of Mr. Trump, led by Senator Ted Cruz, Republican of Texas, have latched onto the resolution of the 1876 dispute as a model, proposing that Congress once again create a 15-member commission to decide the validity of various states’ electors. “We should follow that precedent,” Mr. Cruz and 10 other new or returning Republican senators wrote in a joint statement over the weekend.

But there are also profound differences between that battle and this one. For one, the candidate claiming to be aggrieved this time, Mr. Trump, is the incumbent president with the power of the federal government at his disposal. For another, Mr. Trump’s claims of fraud have proved baseless, universally rejected by Republican and Democratic state election authorities, judges across the ideological spectrum and even by his own attorney general.

In 1876, unlike today, three swing states in the South still occupied by Union troops — Louisiana, South Carolina and Florida — sent competing slates of electors to Washington for Congress to consider. No state has done that this time and every state has certified its results, resulting in a decisive victory for Mr. Biden with 306 electoral votes to 232 for Mr. Trump.

“I don’t really imagine Ted Cruz knows that much about the election of 1876,” said Eric Foner, an emeritus history professor at Columbia University and a leading Reconstruction scholar. “The fundamental difference here is in 1876, there were disputed returns from three states. Today, there’s a lot of talk from Trump and others about fraud, but you don’t have two reports of electoral votes each claiming to be official from the states.”