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The viewport camera has 50mm Focal Length and an aspec ratio depending on your 3d views edge lenghts (as the 3d window is adjustable it could be anything from letterbox to widescreen). So technicly if your camera has the same focal lenght and the same image resolution you should get a 1:1 match either in perspective or orthographic mode.
Here's a screenshot of the viewport camera in the N-Menu.
https://i.imgur.com/MiABPpa.png
If you lock the camera to the viewport and enable passepartout in the camera options, you may have an easier time aligning the camera correctly.