A Taxi Will Cost You The Same Amount for Less Hassle
Copenhagen is a beautiful city, but what takes place below is an absolute train wreck. I've visited cities in a lot of countries and a lot of states, and this has been by far the worst metro system I've ever encountered.
The trains are constantly delayed, and it's recommended that you buy tickets through the app, but there's no stable wifi connection for you to access the app. It seems completely understaffed and if you can somehow get a metro steward to pay attention to you to answer a question, they don't even seem to know what's going on.
DO NOT buy a rejsekort card. It is a tourist trap. There are no clear directions or signage on how to use the card and the scanners, and apparently if you don't check in correctly, your ticket isn't considered valid EVEN IF YOU PAID FOR IT AND CAN PROVE IT. Also, if you have funds leftover, they can only be reimbursed to a Danish bank account, or turned in in-person at specified locations for cash. So if you leave the country, or even the city, you're out of luck.
The fare for an adult is around 24 DKK ($3.50 USD) which is pushing expensive, especially in comparison with many other European metros. And if you receive a "fare evasion" fee, it will be 750 DKK ($100 USD) on top of the ticket that you already paid for. Such a scam.
In my experience, the steward (ID 21252) actually lied to my face when I directly asked him if there was an issue with my prepaid ticket and told me I was fine to get off at my stop. He did not give me any reason for why he requested my passport and started writing down my personal information. When I got off at my stop, he slapped me with a fee and spoke to me in a rude and condescending tone. When I read that I could contest it, he mocked me and said "okay, yeah, you go do that then."
I contested the fee and it took literal weeks for them to come back with the response "we are obligated to treat all passengers equally according to the Joint National Travel Regulations" by which they mean they are obligated to assume and treat all passengers like criminals. So I was forced to pay more than 30x the original fare.
I mentioned the steward's poor behavior in my emails while contesting the fee, and was given no indication that the steward had even been reprimanded.
To the Copenhagen Metro: I am appalled that you would allow your employees to act in this manner. I felt unsafe in the moment, publicly humiliated, and disrespected. It is unacceptable to lie to your passengers. I do not feel that I was treated equally nor fairly by this steward, rather I felt targeted. I have lost respect for this transportation system.
To Potential Travelers: AVOID THE METRO. It'll be better to take a taxi; you'll pay the same amount, but at least you'll be treated better.