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
"""View to show dependencies between DAGs"""
    refresh_interval = timedelta(
        seconds=conf.getint(
            "webserver",
            "dag_dependencies_refresh_interval",
            fallback=conf.getint("scheduler", "dag_dir_list_interval"),
        )
    )
    last_refresh = timezone.utcnow() - refresh_interval
    nodes = []
    edges = []
    @expose('/dag-dependencies')
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG_DEPENDENCIES),
        ]
    )
    @gzipped
    @action_logging
    def list(self):