In VistaVision

As this Hollywood Reporter article mentions, The Searchers was filmed in the VistaVision process, a unique alternative to CinemaScope for directors who didn't want to deal with the wide-and-narrow 'Scope frame. VistaVision was mostly used by Paramount, the only studio that rejected CinemaScope; it wasn't a widescreen process (though the frame could be cropped to a faux-widescreen ratio, the optimal projection width of a VistaVision movie is about 1.85:1), but rather made its effect through the higher quality of the image it produced. At a time when many movies looked visually dull -- in part due to the problems with early CinemaScope lenses -- VistaVision blew you away with how good it looked, as Martin Scorsese explains in the article:

"I (don't have the words to) tell you what that VistaVision looked like projected," he says of the long-gone system that yielded fine grains, endless depths of field and extra-wide images. "There's nothing today that can equal that." The cinematic poet and landscape artist Ford made the most of the format and Technicolor with endless longshots of his beloved Monument Valley.

Unfortunately, Paramount kind of squandered its advantage with VistaVision by making most of its '50s films on the cheap: with their stagy look and use of obvious studio interiors in place of real locations, most of Paramount's VistaVision movies don't take advantage of the format. But The Searchers certainly does; it was Ford's only VistaVision movie, and Warner Brothers' only movie to use the process, and Monument Valley never looked better than it does here. (The reason Ford used the process for this film and this film only was probably that one of the producers of The Searchers, C.V. Whitney, was a big stockholder in Technicolor, and Technicolor was compatible with VistaVision but not CinemaScope.) Alfred Hitchcock also liked VistaVision, which he used not only at Paramount but in the one film he made for MGM, North By Northwest.

The Widescreeen museum has great resources on the history of VistaVision, including this old press release about the advantages of the format. There's also an article about the "wide" version of VistaVision, Technirama.