Facial Recognition Technology Warrant Act of 2019 This bill prohibits, subject to certain exceptions, an officer or employee of a federal agency from using facial recognition technology to engage in ongoing surveillance of one or more individuals unless such efforts support a law enforcement activity for which an appropriate court order has been obtained. It also sets out requirements related to these court orders and testing procedures for facial recognition technology systems used by federal agencies. An individual who has been the subject of ongoing surveillance in violation of this bill may move to suppress information obtained by the surveillance in court, administrative, or similar proceedings.