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If you lose your NemID code card you first cancel it online via your CPR number and your password . Then you order a new one online (identifying yourself via your passport or driving license) and it'll be shipped to the address registered with the CPR card. I have no doubt it's not bulletproof but low-level fraud seems less likely. I'd more concerned about massive irretrievable data loss.
In Denmark you would have had to provide your CPR (sort of Social Security number) AND then use a single use code to sign-0ff the transaction (you're given a 100 of them at a time on a separate document). The CPR works for everything from medical prescriptions to tax, local authorities, online purchases etc... It makes everything easier IMO but obviously it's a bit Big Brother, while your pharmacist cannot access your tax records and the Treasury your doctor's notes I'd imagine the police (or a hacker) could potentially know absolutely everything about you.