Sandborg played the 36 holes in 139 strokes, five under par, and was two strokes behind the 52-year-old veteran and former world number one Lee Westwood, England, who won the qualifying tournament.
Jens Dantorp, ranked 368 in the world, also had the chance to qualify for the British Open on Tuesday but finished outside the top five on the Royal Cinque Ports course.
It is already clear that Henrik Stenson (Sweden's only male major winner to date after the British Open victory at Royal Troon in 2016), Ludvig Åberg, Jesper Svensson and Sebastian Söderberg are qualified for the 153rd edition of the prestigious major which will be decided on 17–20 July.