Copenhagen's public transit card is the Rejsekort.
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Copenhagen uses the Rejsekort. The Rejsekort covers the Metro, S-train, and buses — a City Pass is simpler for short visits.
You can buy it at station machines or 7-Eleven.
Usually yes — it's typically faster than buying paper tickets and often cheaper per ride, even for just a couple of days.
In some cities you can tap a contactless card or phone directly, though it's worth checking current signage or the transit authority's site, since not every system supports it yet.