calling a parent UIViewController method from a child UIViewController

One easy way to achieve this you can use NSNotificationCenter for that.

In your ParentViewController add this into viewDidLoad method:

override func viewDidLoad() {
    super.viewDidLoad()
    NotificationCenter.default.addObserver(self, selector: Selector(("refresh:")), name:NSNotification.Name(rawValue: "refresh"), object: nil)
}

After that add this function in ParentViewController which will get called when you dismiss your ChildViewController:

func refreshList(notification: NSNotification){

    print("parent method is called")
}

and into your ChildViewController add this code where you dismissing your child view:

 @IBAction func btnPressed(sender: AnyObject) {

    NotificationCenter.default.post(name: NSNotification.Name(rawValue: "refresh"), object: nil)
    self.dismiss(animated: true, completion: nil)
}

Now when you dismiss child view refreshList method will be call.

Add a weak property to the child view controller that should contain a reference to the parent view controller

class ChildViewController: UIViewController {
weak var parentViewController: UIViewController?
....
}

Then in your code (I'm assuming it's inside your parent view controller),

let storyboard = UIStoryboard(name: "Main", bundle: nil)
let vc = storyboard.instantiateViewControllerWithIdentifier("myChildView") as! ChildViewController
vc.parentViewController = self
self.presentViewController(vc, animated: true, completion: nil)

And, as vomako said, call the parent's method before dismissing your child view controller.

parentViewController.someMethod()
self.dismissViewControllerAnimated(true, completion: nil)

Or, you can also call the method in the completion paramter of dismissViewControllerAnimated, where it will be run after you child view controller dismisses:

self.dismissViewControllerAnimated(true) {
    parentViewController.someMethod()
}