Given almost claimed a second win when Dandino was second by a head to the favourite Rebel Soldier in the day's big race, the Gordon Stakes.
He told BBC Lincolnshire: "We came agonisingly close to doing the double.
"It would have been lovely for Dandino to have won five races in a row but it's still been a good day for us.
In his previous outing Dandino recorded a maiden Royal Ascot victory for Given and his fourth consecutive win.
And Given added that the three-year-old, ridden by Paul Mulrennan, was shaping up to be a contender for the season's final classic, the St. Leger at Doncaster.
"This race is a very important trial for the St. Leger," he said.
"What we've seen today is a wonderful performance by a horse who's got a definite chance of winning in September."