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 task_instance:
                return None
            
            
            
            task_instance_data = [
                task_instance.state,
                task_instance.try_number,
                None,  
                None,  
            ]
            if task_instance.start_date:
                
                task_instance_data[2] = int(task_instance.start_date.timestamp())
                if task_instance.duration is not None:
                    task_instance_data[3] = truncate_task_duration(task_instance.duration)
            return task_instance_data
        def recurse_nodes(task, visited):