The Danes have gone from strength to strength in the tournament since the trauma of their opening game, in which midfielder Christian Eriksen suffered a cardiac arrest.
Having hammered Wales in the last 16, they impressively dealt with a dangerous and physical Czech side in a competitive last-eight tie played in a red-hot temperature in Azerbaijan.
They led from the fifth minute, when Thomas Delaney evaded his marker to head in from a corner.
A continual threat on the break, they made it 2-0 just before half-time, with Kasper Dolberg volleying in a superb cross from Joakim Maehle to add to the two goals he scored against Wales.
Their momentum was checked early in the second half as Patrik Schick coolly volleyed in his fifth goal of the tournament, taking him level with Portugal’s Cristiano Ronaldo in the race for the Golden Boot.
But Denmark were able to recompose themselves and dig in to ensure the victory and a semi-final at Wembley on Wednesday.
Their opponent will be either England or Ukraine, who play each other in Rome on Saturday evening.