I visited New York last year in September on an ESTA, but I have mislaid my copy. How do I get another copy as I am travelling again to New York in the next couple of weeks?
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Traveling with an ESTA
Do I need to bring a printout or digital copy of my travel authorization to the airport?
No. DHS will be able to communicate a traveler's ESTA status to the carriers. However, DHS recommends that travelers print out the travel authorization application response in order to maintain a record of their traveler authorization application number and to have confirmation of their ESTA status.
U.S. regulation does NOT require a Visa Waiver Program (VWP) traveler to present a printed copy of the ESTA authorization page in order to travel. However, it is recommended that you print a copy for your records. If you applied for ESTA and you have forgotten your application number, you may retrieve the application through the ESTA website by entering the applicants name, date of birth, passport number and passport issuing country.
As mentioned above, you can nonetheless get one at the official ESTA site.
Obligatory pedantry: ESTA is not a visa, at least in the terminology of the United States. It is an authorization that allows you to travel to the US and apply for entry under the Visa Waiver Program (VWP). (Since the VWP is all about relieving people of a visa requirement, it would be illogical and counterproductive to call ESTA a visa.)
As noted by jpatokal in a helpful comment, a printed copy may nonetheless be useful in some situations, particularly with the airline:
The US does not require a printed copy of the ESTA; however, airlines may still ask for it, particularly if you have a complicated itinerary and your first flight is not to the US.
(emphasis in original)