How do I programmatically add a view right under the navigation bar?

You're not calculating the height of the status bar with the navigation bar. In total they are 64, 44 nav bar and 20 for the status bar

Height of status bar is 20.You should consider status bar also while assigning y of your label. Your viewDidAppear should be

override func viewDidAppear(_ animated: Bool) {

    self.label = UILabel(frame: CGRect(x: 0, y: navigationBar.frame.height+20, width: navigationBar.frame.width, height: 100))
    self.label?.translatesAutoresizingMaskIntoConstraints = false
    self.label?.backgroundColor = UIColor.red
    self.label?.text = "label text"
    self.view.addSubview(self.label!)
 }

Hope it helps. Happy Coding!!

Swift

Try this code with NSLayoutConstraint. newView will appear right under NavigationBar

        self.edgesForExtendedLayout = []//Optional our as per your view ladder

        let newView = UIView()
        newView.backgroundColor = .red
        self.view.addSubview(newView)
        newView.translatesAutoresizingMaskIntoConstraints = false
        if #available(iOS 11.0, *) {
            let guide = self.view.safeAreaLayoutGuide
            newView.trailingAnchor.constraint(equalTo: guide.trailingAnchor).isActive = true
            newView.leadingAnchor.constraint(equalTo: guide.leadingAnchor).isActive = true
            newView.topAnchor.constraint(equalTo: guide.topAnchor).isActive = true
            newView.heightAnchor.constraint(equalToConstant: 50).isActive = true
        } else {
            NSLayoutConstraint(item: newView,
                               attribute: .top,
                               relatedBy: .equal,
                               toItem: view, attribute: .top,
                               multiplier: 1.0, constant: 0).isActive = true
            NSLayoutConstraint(item: newView,
                               attribute: .leading,
                               relatedBy: .equal, toItem: view,
                               attribute: .leading,
                               multiplier: 1.0,
                               constant: 0).isActive = true
            NSLayoutConstraint(item: newView, attribute: .trailing,
                               relatedBy: .equal,
                               toItem: view,
                               attribute: .trailing,
                               multiplier: 1.0,
                               constant: 0).isActive = true

                newView.heightAnchor.constraint(equalToConstant: 50).isActive = true
        }