Scale UIView and all its children
I ended up using
self.view.transform = CGAffineTransformScale(CGAffineTransformIdentity, 2, 2);It allowed me to keep the design created in the Interface Builder.
Unfortunately the sharpness of the image suffers in that case, but this is a small price to pay compared to scripting the whole design programmatically.
Update for Swift 3.0
self.view.transform = CGAffineTransform(scaleX: 2.0, y: 2.0)
For Swift 4.0, zoom 2x:
myView.transform = CGAffineTransform.identity.scaledBy(x: 2, y: 2)