A small script to control the letterboxing in Unity. Attached to the main camera

PortraitLetterboxCamera.cs

using UnityEngine;
using UnityEngine.UI;

public class PortraitLetterboxCamera : MonoBehaviour {

  private Camera camera;

  [SerializeField]
  private bool allowOrthographicSizeChange;

  [SerializeField]
  private float cameraOrthographicSize;

  // The Vertical Padding
  [SerializeField]
  private vec2 padding;

  private void Awake() {
    camera = GetComponent<Camera>();

    PerformViewportSizing(padding);
  }

  private void PerformViewportSizing(padding) {

    var padding = padding

    // Target Aspect Ratio
    float targetRatio = (float)Screen.width / (Screen.height - (padding.x + padding.y));

    // Current Aspect Ratio
    float currentRatio = (float)Screen.width / (float)Screen.height;

    // Ratio Between them
    float scaleheight = currentRatio / targetRatio;

    Rect rect = camera.rect;

    if (scaleheight < 1.0f) {
      rect.width = 1.0f;
      rect.height = scaleheight;
      rect.x = 0;
      rect.y = (padding.y / (float)Screen.height);
    } else {
      float scalewidth = 1.0f / scaleheight;
      rect.width = scalewidth;
      rect.height = 1.0f;
      rect.x = (1.0f - scalewidth) / 2.0f;
      rect.y = 0;
    }

    camera.rect = rect;

    if (allowOrthographicSizeChange) {
      camera.orthographicSize = cameraOrthographicSize;
    }
  }
}