(As of March 7, 2018)
Swift 4
let maxFrameHeight = 75
myLabel = UILabel()
myLabel.frame = CGRect(x: 9, y: 9, width: 126, height: maxFrameHeight)
myLabel.text = "my labels text displayed"
myLabel.numberOfLines = 0
myLabel.sizeToFit()
let newFrameHeight = myLabel.frame.size.height
let safeNewHeight = min(newFrameHeight, maxFrameHeight)
myLabel.frame = CGRect(x: 9, y: 9, width: 126, height: safeNewHeight)
This will get the desired outcome, and it will make sure the new height of the UILabel doesn't pass a certain maximum height you desire for this label.