NRS holds the records of the Highland and Island Emigration Society, 1851-1859, which was set up by private subscription to alleviate destitution in the Highlands by promoting and assisting the emigration of Highlanders to Australia. Their passenger lists for the years 1852-1857 have survived and are organised by ship and by family. They record the name, age and residence of each emigrant (National Records of Scotland, HD4/5). You can search the index to the passenger lists online at the Scottish Archive Network website.
NRS also holds records relating to a state aided scheme which was set up in the 1880s to assist emigrants from Harris and Lewis to settle in Manitoba, Canada. The names of the emigrants are listed in the files of the Department of Agriculture and Fisheries (National Records of Scotland, AF51).
For information on sources for Scottish criminals transported to the Americas and Australia from the 17th to the 19th centuries, see the NRS guide on crime and criminals.
Other references to individual emigrants, including correspondence, may be found in a wide variety of records searchable in the NRS' online catalogue. You can enquire about viewing such items by contacting the Historical Search Room.
The National Archives, London (TNA)
Responsibility for emigration in the 19th century lay with the Colonial Office, based in London. Its records are held by TNA. You can search the outward passenger lists, 1890-1960, (The National Archives, BT27), online at Find My Past for lists of passengers leaving the UK and Irish ports and travelling to places such as the USA, Canada, India, New Zealand and Australia. For additional sources please consult TNA's guide on emigration.
Merseyside Maritime Museum
Liverpool was the main port of departure in the 19th century for emigrants from Britain and Europe. The Merseyside Maritime Museum in Liverpool acts as a clearing house for information on sources of emigration.
The National Library of Scotland in Edinburgh holds useful reference sources and some records relating to emigration.
Accounts of the highland clearances and a searchable database can be found at the Clearances website.
The National Archives of Ireland's transportation database, 1791-1853, lists Irish criminals transported to Australia.
Immigration records, such as arrival lists, have been found to provide more comprehensive detail than the departure lists available in Britain.
The Statue of Liberty - Ellis Island website maintain a searchable database of passengers entering the United States through Ellis Island and the Port of New York, 1892-1924, from which you can view the original ships manifest.
A searchable database of passengers entering the United States through Castle Garden Immigration Centre, 1855-1890, can be found at the Castle Garden website.
Please see the NRS' guide on emigration records for suggestions for further reading on this topic.