In the event that Scotland votes for independence in a referendum, what will happen to Scottish representatives at Westminster?
When Montenegro declared independence 13 days after its 2006 referendum, the Serbia-Montenegro joint parliament consisted only on members appointed by the two constituent parliaments, and could simply be dissolved. In 2011, the Southern Sudanese were (rightly) annoyed when their members of the Sudanese parliament were sent packing before the formal declaration of independence after the January referendum but before independence was declared on 9 July. At the other extreme, the MPs elected to the Indonesian parliament to represent East Timor in 1999 kept their seats, despite grumbling, until the 2004 election, although East Timor had become independent in 2002 and their constituency was therefore no longer part of the coutry.
If the Scottish referendum takes place in late 2014, it is entirely possible that subsequent negotiations will take so long that the results may not be implemented until after the next Westminster general election, which is due in May 2015 (and might in any case happen earlier). If Scottish independence is in fact a done deal by then, it would be sensible simply not to hold the 2015 Westminster election in Scotland and instead to prolong the mandates of Scottish MPs until independence day, at which point they would go home. But if the next Westminster election happens before the Scottish referendum, or if there are other unforeseen complications, Scottish MPs could sit at Westminster for years after their constituencies have left the UK.
UK constitutional precedent is certainly in that direction. In the 1918 election, Sinn Fein won 70 of the 75 seats in the twenty-six counties of Ireland which became independent in 1922, the old Nationalist Party won two and Unionists three. The latter five took their seats in the House of Commons, and continued to speak and vote at Westminster until the November 1922 election. Although this was before the formal enactment of Irish independence in December 1922, it was after the assumption of power by the Provisional Government in January, and so the five were representing territory in the UK parliament that was no longer under UK control. If the November 1922 election had been delayed until 1923, they would have continued to sit, like the four East Timorese in the Indonesian parliament, representing constituencies which were no longer legally part of the country.
As for the House of Lords: from 1801 to 1922, peers who held Irish titles elected 28 of their number to serve as Irish Representative Peers at Westminster. The last of these elections was in 1919 when Lord Roden was elected to replace Lord Langford. Ove the following decades the last twenty-eight peers continued to sit in the House of Lords but were not replaced as they died, starting with Lord Curzon in 1925 and ending in 1961 with Lord Kilmorey (whose title, but not his seat, was eventually inherited by Richard Needham who served as a junior minister in Northern Ireland for years). The second last survivor, the Earl of Drogheda, was chairing meetings in the House of Lords until a few days before his death in November 1957, almost 35 years after the southern Irish MPs had left the Commons. (Lord Kilmorey does not appear to have ever spoken in the House of Lords as far as I can tell.)
Scotland's relationship with the House of Lords has changed over the centuries. From 1707 to 1963, Scottish peers convened after every general election to elect sixteen of their number as representative peers in Westminster. From 1963 to 1999, all Scottish peers were entitled to sit in the House of Lords (there are currently 42 of them who do not also hold an English, Great Britain or UK title), and since 1999 they have been eligible for membership like the other hereditary peers.
These days, the House of Lords has become a very peculiar animal. Under the government's current proposals, Scotland would elect seven or eight members of the new House of Lords every five years for fifteen-year terms, and a number of the appointed members would presumably also be Scottish. Since the entire process is going to consist largely of transitional arrangements for the first decade of its operation, I suppose it doesn't tax the imagination too much to find transitional arrangements for Scotland where the Scottish members of the new body are pensioned off after independence day.
But it's much more likely, in my view, that Scottish independence will succeed and the current House of Lords reforms will fail, leaving the UK in the same position it was in in 1922, with a rhetorical commitment to reforming the upper house which has not been implemented and a radically changed constitutional position. I think that Scottish title-holders make up a bit under 10% of the current House of Lords - 9 of the surviving 92 hereditaries (the Countess of Mar, the Earl of Erroll, the Earl of Caithness, the Earl of Lindsay, the Earl of Northesk, the Earl of Dundee, Viscount Falkland, Lady Saltoun, and Lord Reay) have Scottish titles only, though of the life peers whose titles have a Scottish element the proportion may be fewer - only five of the 120 life peers created since the last election have Scottish-based titles (John McFall, Tommy McAvoy, Jack McConnell, Des Browne, and Michael Ancram who holds a whole clutch of titles including Marquess of Lothian), but I also count 3 of Gordon Brown's 34, and 7 of the 77 of Blair's last term (and can't really be bothered to count earlier creations).
Scots in the House of Lords could reasonably cite the precedent of the Earl of Drogheda to argue that they should be allowed to remain in place on the same terms as the other peers, until they gradually die off. I dunno though; that's quite a large chunk of the Upper House whose allegiance nominally would lie in another country. Perhaps, if the current House of Lords reforms fail (as I think they deserve to) and Scottish independence succeeds, it will kickstart a process to find a better upper house for England, Wales and Northern Ireland, which in my view would be a much smaller body of long-term appointed members, with a clear mandate for revision and scrutiny. That is, if such a body is needed at all; I note that there has been no talk of an independent Scotland adopting a bicameral system.
(Incidentally, if you don't already know, you probably will not guess which British-ruled island territory was offered full integration into the UK in 1955, with seats in the House of Commons and all the trimmings, an arrangement which did not get sufficient support in the 1956 referendum to be implemented.)