But after closing with a five-under-par total of 283, he said: "I am not going to change any plans. I'm looking forward to the Walker Cup and it may be another two years before I turn pro."
Saltman, whose grandfather Tommy Younger was the Scotland goalkeeper in the Fifties, edged out Eric Ramsay, a fellow Scot and fellow qualifier, by one shot.
The 19-year-old from near Edinburgh putted up and over the valley of sin from 30 yards to two feet and celebrated as the ball dropped into the hole for a 71.
"I needed that. I saw what Eric shot in the morning and it was a great birdie," Saltman said. "The Walker Cup is my main goal, but winning the medal at the home of golf is a fantastic bonus for me. You have got to enjoy people watching and cheering you on. I got to two under today [and six overall] and then hit a couple of slack shots. That happens."
Yet his Open dreams almost came to a dead stop at the first hurdle - regional qualifying. He finished joint-14th at Renfrew and clinched a place in the final qualifying only through a play-off.
Ramsay set down a difficult marker with a closing 68 and a four-under-par total of 284. When Saltman moved to six under after 12, it seemed that the medal was in the bag. However, he then bogeyed the 13th and 17th to bring him level with Ramsay.
Saltman then showed a maturity beyond his years to get the birdie when needed, with the medal staying in Scotland for a second successive year following Stuart Wilson's victory.
Ramsay, from Carnoustie, chalked up five birdies in a closing 68. "It's been the best experience of my life," he said.
The Italian Edoardo Molinari, two shots adrift of Saltman at the start of play, saved his worst round to last by posting a 75.
The European amateur champion Matthew Richardson, from Middlesex, finished with a four-over-par 76.