Billie Eilish, 17, didn't tell the audience at Coachella on Saturday (20 April) to put their phones away. She asked that if they recorded her next song – When The Party's Over – they didn't look through the screens, but through their own eyes. She reminded everyone that every moment is yours, and never comes again. She pleaded for them to take note of that.

Earlier on in the day, in a tent opposite this stage Maggie Rogers, 24, spoke with similar sentiments. “Let that be something that gives you permission to dance a little harder, to sing a little louder,” she said, of the fleeting nature of our present gifts. “All of this only matters if you let it, so let it in.”

These were Saturday's most precious moments.

Rogers and Eilish are markedly different performers, but both have contended with enormous hype and expectation. Neither Rogers nor Eilish have pandered to the pressures put on young women in the music industry, and both have taken their obsession with traditional singer-songwriting to make confessional music carried by the strength of movement. Rogers' movement is fluid, but tough like a waterfall leaping from a cliff. Eilish's pop-and-lock style is harder and streetwise, like a prowling predator ready to pounce.

It's incredibly moving to look around at Rogers and witness swathes of young women all with glitter painted on their faces, holding each other and mimicking her own hooting and pirouetting. During songs like Fallingwater and Retrograde, there were people with tears streaming down their face in every direction. Towards the latter half of the set, Rogers could barely transition through songs in time, such was the never-ending ovation that accompanied each track's end. “This is unbelievable,” she said, beaming.

“Maggie Rogers is my god,” said one young woman. “Billie Eilish is my cult leader,” said another.

Eilish was also gobsmacked. Lines and lines of young women were pressed up against the barrier even before she came onstage – many shrieking when they saw Justin Bieber escorted into the artist viewing area. This weekend's set went without any hitches. One set piece had to be left out as a result of the brutal winds that threatened the stage. Eilish stood withstanding Mother Nature itself, her hair battering her face. There were palm trees either side of her that were struggling to stay as upright as she was.

Eilish's Coachella story has been one of defiance. Last weekend she emerged victorious, but it wasn't smooth sailing, with technical hitches causing delays and onstage jitters presenting themselves in forgotten lyrics and a mic mishap. This weekend she arrived unstoppable. Eilish was so in her element and so unphazed by the gusty conditions, she said: “If I could stay up on this stage forever, I would.”

Both of these sets were rooted in a fundamental sense of relatability, which made for an inspired sea of female onlookers celebrating their own lives by watching their stories re-told by their musical leaders on stage. “Maggie Rogers is my god,” said one young woman. “Billie Eilish is my cult leader,” said another. The lack of equal representation among the genders is still a chronic issue for mainstream music festivals, but to give credit where it's due, Coachella hasn't just booked a myriad of world-class female performers, it's given them the slots they've earned.

Both artists didn’t take this for granted. For Rogers, you sense she held back the tears throughout her hour. For Eilish, she couldn't quite keep it in towards the end. She turned the mic on the crowd when she began to get choked up. “And I could lie, say I like it like that, like it like that,” the crowd sang, helping her out. Speechless, she smiled at all her eyes could see. “I love you,” she cried, from the bottom of her heart, and then uttered an expletive. But expletives were perhaps the most effective way to express what took place in these venues. On Saturday night, milestones were set for a new generation's icons, who were made by the people for the people.

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