If you have Danish roots, this site could be a helpful place to start.
According to the web site information, there were a number of scandals prior to 1868 in which unsuspecting emigrants were conned by Danish emigration agents. So the Danish parliament passed regulations that year requiring the Copenhagen Chief of Police to approve and monitor all emigration agents in Denmark. Subsequently, he was also required to authorize all overseas tickets made out in Denmark. The information from each ticket was copied down in ledgers, and thus became the Copenhagen Police Records of Emigrants. A total of 90 thick volumes were compiled but are difficult to use.
In 1990 the Danish Emigration Archives began compiling a database including all the information provided in the police records for all Danish emigrants. Currently the database contains records for 394,000 persons who emigrated from May 24, 1868, to December 1908.
Source: The Provincial Archives of Sealand, Copenhagen Police Records of Emigrants 1868-1940: no. 21-58 Direct emigrants; 198-248 Indirect emigrants; 59-196 Ships sailings with passenger lists.
Be sure to read the FAQ on the site for more insight into the database and how to do an effective search.