WASHINGTON — It has been 86 years since Hattie Wyatt Caraway of Arkansas became the first woman elected to the United States Senate, and women remain woefully underrepresented in the chamber. Women make up nearly 51 percent of the United States population but just 23 percent of the Senate, an all-time high, nonetheless, after Cindy Hyde-Smith was sworn in as the new senator from Mississippi this month .

They form something of a tight-knit club.

They have bipartisan dinners that make their male colleagues jealous. They have banded together to solve seemingly intractable problems; in 2013, when Senator Ted Cruz, Republican of Texas, led a move to shut down the government, the women of the Senate cut a bipartisan deal to reopen it. And they have pushed their colleagues to tackle issues like sexual harassment, domestic violence and sexual assault in the military.

On Sunday, four female senators — Susan Collins, Republican of Maine, Heidi Heitkamp, Democrat of North Dakota, Amy Klobuchar, Democrat of Minnesota, and Joni Ernst, Republican of Iowa — discussed women in politics, public policy, and the special bond among women in the Senate at a TimesTalks forum in New York. (Ms. Ernst, waylaid by an Iowa snowstorm, arrived toward the end.)

Here are some of the session’s lighter moments, offering a peek behind the scenes of life as a woman in the Senate:

Who me? Run for public office?

Ms. Collins says she is often called upon to recruit women (and men) who are thinking of running for office. Many women tell her that they do not feel quite ready. “I have never, ever had a man say that to me, that he wasn’t quite ready,” she said, adding, “I think there’s a self-doubt and a hesitancy to take risks that we need to overcome.”