If your ancestors emigrated after 1868 you may be able to find information regarding them in the Copenhagen Police Records of Emigrants. They would, however, only be listed if they purchased a contract-ticket from an Emigration Agent with an office in Copenhagen.
The records kept by the Police were not actually of the emigrants themselves - but rather, of all contracts signed between agents and emigrants. This was done to prevent "crooked" agents from cheating emigrants by taking their money and then "forgetting" to purchase the tickets or help with travel arrangements, etc.
If your ancestor - for any reason - travelled independently, you will not find their name listed in the Record of Emigrants! Most people, but not all, contracted with an agent. Sometimes one or two family members (perhaps a father and a grown son, or two brothers, etc.) would be the first to emigrate, and they would later send tickets for the rest of the family.
See and search an online emigration list:
If you find your ancestor listed in the emigration records, you will also find the following information:
Full name
Occupation
Place of birth and last place of residence
Age
Destination
Contract number
Date of listing in the Copenhagen Police Records of Emigrants
Name of the ship
