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
if not dag:
            flash(f'DAG "{dag_id}" seems to be missing from DagBag.', "error")
            return redirect(url_for('Airflow.index'))
        root = request.args.get('root')
        if root:
            dag = dag.partial_subset(task_ids_or_regex=root, include_downstream=False, include_upstream=True)
        num_runs = request.args.get('num_runs', type=int)
        if num_runs is None:
            num_runs = conf.getint('webserver', 'default_dag_run_display_number')
        try:
            base_date = timezone.parse(request.args["base_date"])
        except (KeyError, ValueError):
            base_date = dag.get_latest_execution_date() or timezone.utcnow()
        with create_session() as session:
            dag_runs = (
                session.query(DagRun)
                .filter(DagRun.dag_id == dag.dag_id, DagRun.execution_date <= base_date)
                .order_by(DagRun.execution_date.desc())
                .limit(num_runs)
                .all()
            )
        dag_runs = {dr.execution_date: alchemy_to_dict(dr) for dr in dag_runs}
        max_date = max(dag_runs.keys(), default=None)
        form = DateTimeWithNumRunsForm(
            data={
                'base_date': max_date or timezone.utcnow(),
                'num_runs': num_runs,
            }
        )
        doc_md = wwwutils.wrapped_markdown(getattr(dag, 'doc_md', None))