In the UI it would be nice to duplicate the selected connection, in the menu "With Selected". 

The copy would be set with the same name plus some suffix (_copy, _1, whatever) and it is useful for when you have a connection with all equal fields except something in a particular one. 
airflow/www/views.py
"""Shows task instances."""
        dag_id = request.args.get('dag_id')
        dag = current_app.dag_bag.get_dag(dag_id)
        dttm = request.args.get('execution_date')
        if dttm:
            dttm = timezone.parse(dttm)
        else:
            return "Error: Invalid execution_date"
        task_instances = {ti.task_id: alchemy_to_dict(ti) for ti in dag.get_task_instances(dttm, dttm)}
        return json.dumps(task_instances, cls=utils_json.AirflowJsonEncoder)
    @expose('/object/tree_data')
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
        ]
    )
    @action_logging
    def tree_data(self):