This solution works for me:
let rootViewController: UIViewController =
UIApplication.sharedApplication().windows.lastObject.rootViewController!!
rootViewController.presentViewController(alert, animated: true, completion: nil)
edit by @galambalazs: The reason it works is because:
You can grab the window with the current highest window level and present your View Controller inside that Window (making it the top View Controller in the top Window).
UIApplication.sharedApplication().windows
The windows in the array are ordered from back to front by window level;
thus, the last window in the array is on top of all other app windows.
Also you might want to set the tintColor of that window so that it matches your apps global tintColor.
UIWindow *topWindow = [UIApplication sharedApplication].windows.lastObject;
// we inherit the main window's tintColor because topWindow may not have the same
topWindow.tintColor = [UIApplication sharedApplication].delegate.window.tintColor;
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