Palpatine kills Padme
"It seems in your anger, you killed her." -Palpatine to Vader when asked about Padme's status
How was it that Palpatine knew of Padme's death so quickly? Her death and the scene above happen simultaneously. One answer I could think of is that Palpatine killed Padme with the Force over a distance. Remember, the medical droid stated that they were losing Padme for unknown reasons. The unknown reason could've been Palpatine's Force power.
And when thinking about this, it somewhat makes sense. We all know that anger is a big part of a Sith Lord's strength... so, in order to infuriated Vader even more, Palpatine could've caused death to fall over Padme, thus making Vader even more powerful. Palpatine knew that all Anakin wanted out of the Dark Side was to save his wife. And so to create that sort of irony for Vader would've been the perfect ingenius plan.