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
else:
        
        
        base_date = (date_time + timedelta(seconds=1)).replace(microsecond=0)
    default_dag_run = conf.getint('webserver', 'default_dag_run_display_number')
    num_runs = www_request.args.get('num_runs', default=default_dag_run, type=int)
    drs = (
        session.query(DagRun)
        .filter(DagRun.dag_id == dag.dag_id, DagRun.execution_date <= base_date)
        .order_by(desc(DagRun.execution_date))
        .limit(num_runs)
        .all()
    )
    dr_choices = []
    dr_state = None
    for dr in drs:
        dr_choices.append((dr.execution_date.isoformat(), dr.run_id))
        if date_time == dr.execution_date:
            dr_state = dr.state
    
    if not dr_state and drs:
        dr = drs[0]
        date_time = dr.execution_date
        dr_state = dr.state
    return {
        'dttm': date_time,
        'base_date': base_date,
        'num_runs': num_runs,
        'execution_date': date_time.isoformat(),
        'dr_choices': dr_choices,