All national museums in Denmark have a free access policy for young persons under the age of 18. They are:
National Gallery of Denmark, Copenhagen 
National Museum of Denmark, Copenhagen 
Open Air Museum, Lyngby 
Danish Music Museum, Copenhagen 
Post and Telegraph Museum, Copenhagen 
Ny Carlsberg Glyptotek, Copenhagen 
Royal Arsenal Museum, Copenhagen 
The Hirschsprung Collection, Copenhagen 
Danish Museum of Hunting and Forestry, Hørsholm 
Royal Danish Naval Museum, Copenhagen 
Thorvaldsen Museum, Copenhagen 
Museum of Copenhagen, Copenhagen 
Dansk Landbrugsmuseum (Danish Agricultural Museum), Auning 
There are many other museums across Denmark that operate a free entry for kids policy. Please consult your local tourist office for more details.
Free or cheap cinema and theatre
Keep an eye out for Festival - Theatre for Young Audiences in Denmark , that offers a world of theatre experiences. The festival takes place different cities from year to year. In Copenhagen there’s a free puppet show in Kongens Have , in Odense there’s the HC Andersen Parade . If you’re looking for free cinema, one place to check out is the Film House & Cinematec  in Copenhagen, where films are shown all weekdays for free for kids aged 3-6. It is also worth checking out local libraries across Denmark, as they often organise special events for kids.
Free events for kids
All year round, but especially in the summer months, there’s a wealth of free events for kids and young people - harbour and city festivals, historical markets and much more. Contact your local tourist office for up to date details.