Present modal view controller in half size parent controller

You can use a UIPresentationController to achieve this.

For this you let the presenting ViewController implement the UIViewControllerTransitioningDelegate and return your PresentationController for the half sized presentation:

func presentationController(forPresented presented: UIViewController, presenting: UIViewController?, source: UIViewController) -> UIPresentationController? {
    return HalfSizePresentationController(presentedViewController: presented, presenting: presentingViewController)
}

When presenting you set the presentation style to .Custom and set your transitioning delegate:

pvc.modalPresentationStyle = .custom
pvc.transitioningDelegate = self

The presentation controller only returns the frame for your presented view controller:

class HalfSizePresentationController: UIPresentationController {
    override var frameOfPresentedViewInContainerView: CGRect {
        guard let bounds = containerView?.bounds else { return .zero }
        return CGRect(x: 0, y: bounds.height / 2, width: bounds.width, height: bounds.height / 2)
    }
}

Here is the working code in its entirety:

class ViewController: UIViewController, UIViewControllerTransitioningDelegate {

    @IBAction func tap(sender: AnyObject) {
        let storyboard = UIStoryboard(name: "Main", bundle: nil)
        let pvc = storyboard.instantiateViewController(withIdentifier: "CustomTableViewController") as! UITableViewController

        pvc.modalPresentationStyle = .custom
        pvc.transitioningDelegate = self
        pvc.view.backgroundColor = .red

        present(pvc, animated: true)
    }
    
    func presentationController(forPresented presented: UIViewController, presenting: UIViewController?, source: UIViewController) -> UIPresentationController? {
        return HalfSizePresentationController(presentedViewController: presented, presenting: presentingViewController)
    }
}

class HalfSizePresentationController: UIPresentationController {
    override var frameOfPresentedViewInContainerView: CGRect {
        guard let bounds = containerView?.bounds else { return .zero }
        return CGRect(x: 0, y: bounds.height / 2, width: bounds.width, height: bounds.height / 2)
    }
}

Jannis captured the overall strategy well. It didn't work for me in iOS 9.x with swift 3. On the presenting VC, the action to launch the presented VC is similar to what was presented above with some very minor changes as below:

let storyboard = UIStoryboard(name: "Main", bundle: nil)
let pvc = storyboard.instantiateViewController(withIdentifier: "SomeScreen") as SomeViewController

pvc.modalPresentationStyle = .custom
pvc.transitioningDelegate = self

present(pvc, animated: true, completion: nil)

To implement UIViewControllerTransitioningDelegate on the same presenting VC, the syntax is quite different as highlighted in SO answer in https://stackoverflow.com/a/39513247/2886158. This is was the most tricky part for me. Here is the protocol implementation:

func presentationController(forPresented presented: UIViewController, presenting: UIViewController?, source: UIViewController) -> UIPresentationController? {
    return HalfSizePresentationController(presentedViewController:presented, presenting: presenting)
}

For the UIPresentationController class, I had to override the variable frameOfPresentedViewInContainerView, not method, as below:

class HalfSizePresentationController: UIPresentationController {
    override var frameOfPresentedViewInContainerView: CGRect {
        return CGRect(x: 0, y: 0, width: containerView!.bounds.width, height: containerView!.bounds.height/2)
    }
}

There were some questions about how to dismiss the view after presentation. You can implement all the usual logic on your presented VC like any other VC. I implementation an action to dismiss the view in SomeViewController when a user tabs outside the presented VC.

It would be a a clean architect if you push some delegate methods of UIViewControllerTransitioningDelegate in your ViewController that want to be presented as half modal.

Assuming we have ViewControllerA present ViewControllerB with half modal.

in ViewControllerA just present ViewControllerB with custom modalPresentationStyle

func gotoVCB(_ sender: UIButton) {
    let vc = ViewControllerB()
    vc.modalPresentationStyle = .custom
    present(vc, animated: true, completion: nil)
}

And in ViewControllerB:

import UIKit

final class ViewControllerB: UIViewController {

lazy var backdropView: UIView = {
    let bdView = UIView(frame: self.view.bounds)
    bdView.backgroundColor = UIColor.black.withAlphaComponent(0.5)
    return bdView
}()

let menuView = UIView()
let menuHeight = UIScreen.main.bounds.height / 2
var isPresenting = false

init() {
    super.init(nibName: nil, bundle: nil)
    modalPresentationStyle = .custom
    transitioningDelegate = self
}

required init?(coder aDecoder: NSCoder) {
    fatalError("init(coder:) has not been implemented")
}

override func viewDidLoad() {
    super.viewDidLoad()
    
    view.backgroundColor = .clear
    view.addSubview(backdropView)
    view.addSubview(menuView)
    
    menuView.backgroundColor = .red
    menuView.translatesAutoresizingMaskIntoConstraints = false
    menuView.heightAnchor.constraint(equalToConstant: menuHeight).isActive = true
    menuView.bottomAnchor.constraint(equalTo: view.bottomAnchor).isActive = true
    menuView.leadingAnchor.constraint(equalTo: view.leadingAnchor).isActive = true
    menuView.trailingAnchor.constraint(equalTo: view.trailingAnchor).isActive = true
    
    let tapGesture = UITapGestureRecognizer(target: self, action: #selector(ViewControllerB.handleTap(_:)))
    backdropView.addGestureRecognizer(tapGesture)
}

@objc func handleTap(_ sender: UITapGestureRecognizer) {
    dismiss(animated: true, completion: nil)
}
}

extension ViewControllerB: UIViewControllerTransitioningDelegate, UIViewControllerAnimatedTransitioning {
func animationController(forPresented presented: UIViewController, presenting: UIViewController, source: UIViewController) -> UIViewControllerAnimatedTransitioning? {
    return self
}

func animationController(forDismissed dismissed: UIViewController) -> UIViewControllerAnimatedTransitioning? {
    return self
}

func transitionDuration(using transitionContext: UIViewControllerContextTransitioning?) -> TimeInterval {
    return 1
}

func animateTransition(using transitionContext: UIViewControllerContextTransitioning) {
    let containerView = transitionContext.containerView
    let toViewController = transitionContext.viewController(forKey: UITransitionContextViewControllerKey.to)
    guard let toVC = toViewController else { return }
    isPresenting = !isPresenting
    
    if isPresenting == true {
        containerView.addSubview(toVC.view)
        
        menuView.frame.origin.y += menuHeight
        backdropView.alpha = 0
        
        UIView.animate(withDuration: 0.4, delay: 0, options: [.curveEaseOut], animations: {
            self.menuView.frame.origin.y -= self.menuHeight
            self.backdropView.alpha = 1
        }, completion: { (finished) in
            transitionContext.completeTransition(true)
        })
    } else {
        UIView.animate(withDuration: 0.4, delay: 0, options: [.curveEaseOut], animations: {
            self.menuView.frame.origin.y += self.menuHeight
            self.backdropView.alpha = 0
        }, completion: { (finished) in
            transitionContext.completeTransition(true)
        })
    }
}
}

The result:

All code is published at my Github

Just in case someone is looking to do this with Swift 4, as I was.

class MyViewController : UIViewController {
    ...
    @IBAction func dictionaryButtonTouchUp(_ sender: UIButton) {
        let modalViewController = ...
        modalViewController.transitioningDelegate = self
        modalViewController.modalPresentationStyle = .custom

        self.present(modalViewController, animated: true, completion: nil)
    }
}

extension MyViewController : UIViewControllerTransitioningDelegate {
    func presentationController(forPresented presented: UIViewController, presenting: UIViewController?, source: UIViewController) -> UIPresentationController? {
        return HalfSizePresentationController(presentedViewController: presented, presenting: presenting)
    }
}

Where the HalfSizePresentationController class is composed of:

class HalfSizePresentationController : UIPresentationController {
    override var frameOfPresentedViewInContainerView: CGRect {
        get {
            guard let theView = containerView else {
                return CGRect.zero
            }

            return CGRect(x: 0, y: theView.bounds.height/2, width: theView.bounds.width, height: theView.bounds.height/2)
        }
    }
}

Cheers!