It is free to register a sole proprietorship and small personal owned company (PMV). A fee must be paid for registration of a public limited company (A/S), private limited company (ApS), an entrepreneurial company (IVS) and other capital companies. Registration requires you to have a Danish social security number (CPR) as well as the Danish Nem-ID.
You can register your foreign company in Denmark for VAT, excise duty, for import/export, or as an employer. Registration does not require for you to have a Danish social security number (CPR).
If you provide a temporary service in Denmark, you have to notify your company details to the Register of Foreign Service Providers (RUT). Foreign service providers (employees and self-employed) working in Denmark must register in RUT.