What proves that you have taken out a motor liability insurance for your vehicle?

You answered correctly. A valid insurance number plate and evidence of insurance both prove that you have motor liability insurance for your vehicle in Germany. The insurance number plate is especially important for vehicles like mopeds or small motorcycles, which receive a special colored plate each year to confirm insurance coverage. Evidence of insurance, such as the insurance certificate, is also accepted proof. The permit for use (Betriebserlaubnis) is only a technical document confirming that your vehicle meets legal requirements to be on the road, but it does not prove insurance. In any check by the authorities, you must be able to prove insurance with the insurance plate or the insurance certificate, never just by showing the Betriebserlaubnis. Remember this rule when asked how to prove insurance.