Okay I hate when I see this everywhere ..."she died of a broken heart..." Or "she lost the will to live .." That's NOT what actually happened !!
.

This is how she actually died..

Palpatine is killing her

Specifically, while fighting Yoda, he (Palpatine) sensed that Anakin was in danger, and began a process that would both kill Padme, and finally, utterly turn Anakin into Darth Vader.

While he is restoring Anakin's body to working (robotic) order after his ordeal on Mustafar, Palpatine uses Padme's life force to keep him alive. That's right, at a distance, the supremely powerful Sith lord taps into the very energy of Padme's connection to 'the living force,' and strips it away from her.

What DID Kill Padme?

Well the medical droid doesn't actually say she's dying of a broken heart, and there's not actually all that much evidence that Anakin's force choking of her was a direct cause either.

Instead, the medical droid turns to Obi Wan, and says:

DROID "Medically, she's completely healthy. For reasons we can't explain, we're losing her."
OBI-WAN "She's dying?!"
DROID "We don't know why. She's lost the will to live. We need to operate quickly if we are to save the babies."
And, Tavano suggests, there is only one thing that could plausibly be causing her to die without seriously advanced medical science being able to work out why.

The Force.

That's right...

The Force is Killing Padme

She has, essentially, had her connection the 'the living force' severed, leaving her inexplicably, but inevitably, dying.

But why is that happening?

Which Means Anakin Also Takes Padme's Life

And, this whole conversation, after Vader rises?

PALPATINE "Lord Vader, can you hear me?"
VADER "Yes master. Where is Padmé? Is she safe? Is she alright?"
PALPATINE "It seems, in your anger, you killed her."
VADER "I–I couldn't have. She was ALIVE–I FELT IT."
{Palpatine knowingly smiles}
VADER "No..."
That's Palpatine being completely honest - since Anakin did, technically, take her life force - and simultaneously lying through his teeth.

How Else Could Palpatine Have Known That Padme Was Dead?

After all, if Anakin - who had a closer connection to her than anyone else in the galaxy - couldn't instantly tell that she was gone, how would Palpatine know?

Unless, of course, he was directly connected to her life force, and felt it be extinguished...by his own actions.

And so, Palpatine had his apprentice, and in that moment of Anakin's utter despair, he had his full, unbending - yet stolen - trust and commitment.