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
"""Dag statistics."""
        dr = models.DagRun
        allowed_dag_ids = current_app.appbuilder.sm.get_accessible_dag_ids(g.user)
        dag_state_stats = session.query(dr.dag_id, dr.state, sqla.func.count(dr.state)).group_by(
            dr.dag_id, dr.state
        )