The Member of the Scottish Parliament for Ettrick, Roxburgh and Berwickshire, John Lamont, says he's relieved that Scotland voted No.
Mr Lamont says he was very worried about the consequences of a Yes vote on The Borders given the proximity to England.
Both sides in the referendum debate spoke about the result in Dumfries and Galloway in the early hours of Friday morning.
David Cameron said that England, Wales and Northern Ireland should also be given the opportunity for their rights to be "enhanced".
The Prime Minister called for a "new and fair settlement for all parts of the UK".
"We have heard the voice of Scotland. Now the millions of voices of England must also be heard," Cameron said.
"Just as Scotland will vote separately in the Scottish parliament on their issues of tax, spending and welfare, so too England, as well as Wales and Northern Ireland, should be able to vote on these issues."
The Scotland Office minister and Conservative MP for Dumfriesshire, Clydesdale and Tweeddale David Mundell says the country now needs stability
"We've got to respect the hundreds of thousands of people who voted yes. I think by bringing forward the additional powers for the Scottish parliament I think that has the scope to address some of the concerns that underlaid why some people voted yes or considered voting yes.
I think it will be possible, relatively straight-forwardly to achieve a consensus on a package of powers because what I think people in Scotland now want is constitutional stability."
David Cameron has congratulated Alex Salmond on a "hard-fought campaign".
I've just spoken to Alex Salmond, congratulating him on a hard-fought campaign. I'm delighted the SNP will join talks on further devolution.
The leader of the Better Together campaign, Alistair Darling, has called the result a "momentous result for Scotland and also the United Kingdom as a whole".
He said that it "reaffirmed all that we have in common and the bonds that tie us together - let them never be broken".
But he said the surge in support for independence showed great dissatisfaction and that "every politician must now listen to their cry for change".
Alex Salmond has said he accepts the No verdict of the Scottish people and called on all Scots to do the same.
Scotland's First Minister said the 1.6 million Yes voters was still a "substantial vote for Scottish independence and the future of the country".
As Scotland looks ahead Salmond say they now expected Westminster to honour its pledge of more powers "with rapid force".
With one result to come in the Highland area this is the tally of the votes:
Yes - 1,539,839 (44.6%)
No - 1,914,187 (55.4%)
No majority of 374,378
Scotland's deputy first minister Nicola Sturgeon has said she will "certainly work with anybody in any way to deliver ... empowerment" for Scotland.
She told BBC News that she remained skeptical of the timetable for devolution that was set out by the three pro-union parties.
She said that yesterday's referendum showed there was a "strong demand for change".
"My party will always seek to do the best for Scotland," she added.
- Aberdeen votes NO by 58.6% to 41.4% YES
- Angus votes NO by 56.3% to 43.7% YES
- East Ayrshire votes NO by 52.8% to 47.2 YES
- East Dunbartonshire votes NO by 61.2% to 38.8% YES
- East Renfrewshire votes NO by 63.2% to 36.8% YES
- Glasgow votes YES by 53.5% to 46.5% NO
- North Ayrshire votes NO by 51.0% to 49.0% YES
- North Lanarkshire votes YES by 51.1% to 48.9% NO
- Perth & Kinross votes NO by 60.2% to 39.8% YES
- South Ayrshire votes NO by 57.9% to 42.1% YES
- South Lanarkshire votes NO by 54.7% to 45.3% YES
- West Lothian votes NO by 55.2% to 44.8% YES