Charles Smith, 89, and Andrew Ramsay, 90, both from Penicuik, are members of veterans' charity Scottish War Blinded, and were awarded the medals at the charity's Linburn day centre in Wilkieston, West Lothian.
The Arctic Star recognises the severity of the conditions experienced by those who served escorting convoys or participated in operations north of the Arctic Circle during the Second World War.
It took a campaign by veterans which lasted several years before the government agreed to award them a medal for surviving the freezing conditions.
Minister of State for Defence Personnel, Welfare and Veterans Mark Francois said: "All those who served our country on the Arctic convoys deserve nothing but the utmost respect and admiration from us.
"I am delighted that these special individuals will receive the Arctic Star that they have so long deserved."
Captain Chris Smith, Naval Regional Commander for Scotland and Northern Ireland presented the medals.
He said: "The journeys undertaken by the men and their ships as part of the Arctic Convoys were fraught with danger.
"As well as an ever-present threat of enemy fire from both surface ships and U-Boats, the weather was a formidable adversary, with freezing conditions and mountainous seas. Many, many ships were lost and thousands of sailors perished.
"It was war at its harshest and Charles, Andrew and their fellow sailors - both military and merchant navy - deserve the respect and admiration of us all for this most dangerous of missions which played a key role in the ultimate defence of our nation. We owe them all a great debt of thanks."
Mr Smith served aboard HMS Palomares and Norfolk during the campaign while Mr Ramsay served aboard HMS Formidable.