how can i increase the height of an inputAccessoryView

Fast forward to 2020, you can just do the following, everything else the same as in maxkonovalov's answer

override var intrinsicContentSize: CGSize {
    return .zero
}

// MARK: UITextViewDelegate

func textViewDidChange(_ textView: UITextView) {
    sizeToFit()
}

To make input accessory view grow vertically you just set its autoresizingMask = .flexibleHeight, calculate its intrinsicContentSize and let the framework do the rest.

The code:

class InputAccessoryView: UIView, UITextViewDelegate {

    let textView = UITextView()

    override init(frame: CGRect) {
        super.init(frame: frame)

        // This is required to make the view grow vertically
        self.autoresizingMask = UIView.AutoresizingMask.flexibleHeight

        // Setup textView as needed
        self.addSubview(self.textView)
        self.textView.translatesAutoresizingMaskIntoConstraints = false
        self.addConstraints(NSLayoutConstraint.constraints(withVisualFormat: "H:|[textView]|", options: [], metrics: nil, views: ["textView": self.textView]))
        self.addConstraints(NSLayoutConstraint.constraints(withVisualFormat: "V:|[textView]|", options: [], metrics: nil, views: ["textView": self.textView]))

        self.textView.delegate = self

        // Disabling textView scrolling prevents some undesired effects,
        // like incorrect contentOffset when adding new line,
        // and makes the textView behave similar to Apple's Messages app
        self.textView.isScrollEnabled = false
    }

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

    override var intrinsicContentSize: CGSize {
        // Calculate intrinsicContentSize that will fit all the text
        let textSize = self.textView.sizeThatFits(CGSize(width: self.textView.bounds.width, height: CGFloat.greatestFiniteMagnitude))
        return CGSize(width: self.bounds.width, height: textSize.height)
    }

    // MARK: UITextViewDelegate

    func textViewDidChange(_ textView: UITextView) {
        // Re-calculate intrinsicContentSize when text changes
        self.invalidateIntrinsicContentSize()
    }

}