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
base_date = request.args.get('base_date')
        num_runs = request.args.get('num_runs', default=default_dag_run, type=int)
        if base_date:
            base_date = timezone.parse(base_date)
        else:
            base_date = dag.get_latest_execution_date() or timezone.utcnow()
        dates = dag.date_range(base_date, num=-abs(num_runs))
        min_date = dates[0] if dates else timezone.utc_epoch()
        root = request.args.get('root')
        if root:
            dag = dag.partial_subset(task_ids_or_regex=root, include_upstream=True, include_downstream=False)
        chart_height = wwwutils.get_chart_height(dag)
        chart = nvd3.lineChart(
            name="lineChart",
            x_is_date=True,
            y_axis_format='d',
            height=chart_height,
            chart_attr=self.line_chart_attr,
        )
        for task in dag.tasks:
            y_points = []
            x_points = []
            for ti in task.get_task_instances(start_date=min_date, end_date=base_date):
                dttm = wwwutils.epoch(ti.execution_date)
                x_points.append(dttm)
                
                y_points.append(ti.prev_attempted_tries)
            if x_points:
                chart.add_serie(name=task.task_id, x=x_points, y=y_points)
        tis = dag.get_task_instances(start_date=min_date, end_date=base_date)