Here's what I do (roughly). Note that this code only checks the top and bottom of the screen, because in my game the player never leaves the center of the screen (horizontally). Also, I'm using a ratio because I want the player to be able to get to a certain point before the camera starts to follow him- I never want the player to completely leave the screen.. so there's a bit of an edge 'safe frame' that I'm checking.

bool SafeFrameCheck()
    {

       Vector3 screenPos = _cameraRef.WorldToScreenPoint(Player.Instance.xform.position);
       float ratio = screenPos.y / _cameraRef.pixelHeight;

       if(ratio < 0f) // if we're below our safe frame
         return false;

       if(ratio > .7f) // if we're above our safe frame, return false       
         return false;    

       return true;    // we're inside our safe frame.
    }