Covidresults.dk offers PCR test for COVID-19 for non-Danish citizens.
You can find all PCR test stations in Denmark here. You can show up at many test stations without an appointment. As a non-Danish citizen, you have to register on Covidresults.dk before meeting up at the test centre. To create an account choose “Sign up” and then enter your email.
Documentation for the test result can be downloaded or printed from this website.
Find further instructions here