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
"""Retrieve log."""
        dag_id = request.args.get('dag_id')
        task_id = request.args.get('task_id')
        execution_date = request.args.get('execution_date')
        dttm = timezone.parse(execution_date)
        form = DateTimeForm(data={'execution_date': dttm})
        dag_model = DagModel.get_dagmodel(dag_id)
        ti = (
            session.query(models.TaskInstance)
            .filter(
                models.TaskInstance.dag_id == dag_id,
                models.TaskInstance.task_id == task_id,
                models.TaskInstance.execution_date == dttm,
            )
            .first()
        )
        num_logs = 0