Few countries still require a Covid-19 certificate, although some require some form of vaccination certificate or a test before departure.
You should check which requirements apply for each country on the Ministry of Foreign Affairs' travel information service (regjeringen.no, in Norwegian), or in the Reiseklar app (regjeringen.no, in Norwegian).
Proof of Covid-19 vaccination
If you need proof of vaccination for your destination, go to Vaccination and print out documentation about any vaccines you have been given in Norway.
Documentation on negative test
If you need documentation on not being ill, you have to pay for this yourself, for example at a private practitioner. The GP mainly does not offer a Covid-19 test for documentation.