CustomSegue.swift

//
//  ModalSegue.swift
//  HabitTracker
//
//  Created by Eivind Lindbråten on 03.09.2017.
//  Copyright © 2017 Eivind Lindbråten. All rights reserved.
//

import UIKit

class ModalSegue: UIStoryboardSegue {

    override func perform() {
        // Assign the source and destination views to local variables.
        let firstVCView = self.source.view as UIView!
        let secondVCView = self.destination.view as UIView!
        
        // Get the screen width and height.
        let screenWidth = UIScreen.main.bounds.size.width
        let screenHeight = UIScreen.main.bounds.size.height
        
        // Specify the initial position of the destination view.
        secondVCView?.frame = CGRect(x: 0.0, y: screenHeight, width: screenWidth, height: screenHeight)
        
        // Access the app's key window and insert the destination view above the current (source) one.
        let window = UIApplication.shared.keyWindow
        window?.insertSubview(secondVCView!, aboveSubview: firstVCView!)
        
        // Animate the transition.
        UIView.animate(withDuration: 0.4, animations: { () -> Void in
            //firstVCView?.frame = (firstVCView?.frame.offsetBy(dx: 0.0, dy: -screenHeight))!
            secondVCView?.frame = (secondVCView?.frame.offsetBy(dx: 20.0, dy: -screenHeight + 40.0))!
            
            // TODO: Let it keep this size?!
            let rect = CGSize(width: screenWidth - 40.0, height: screenHeight - 40.0)
            secondVCView?.frame.size = rect
            
            secondVCView?.layer.shadowColor = UIColor.black.cgColor
            secondVCView?.layer.shadowOpacity = 0.5
            secondVCView?.layer.shadowRadius = 8.0
            secondVCView?.layer.shadowOffset = CGSize(width: 0, height: 3)
            secondVCView?.clipsToBounds = false
            
            
        }) { (Finished) -> Void in
            self.source.present(self.destination as UIViewController, animated: false,                                                            completion: nil)
        }
        
    }
    
}

Something like this: