During the occupation of Denmark, Quistgaard was connected to "Hjemmefronten" og Special Operations Executive for whom he was a contact person and courier. He scouted for new airdrop sites, helped found the Hvidsten group as well as participating in their initial airdrop receptions. Quistgaard and his wife provided support for Special Operations Executive operatives organized by British Intelligence. Additionally Quistgaard participated in the reception of allied airdropped weapons in the area of Gyldenløves Høj. On several occasions Quistgaard demanded that one SOE operative, an Englishman who had parachuted into Denmark, should be returned as inadequate. During a subsequent interrogation of this operative by the Gestapo, he identified Quistgaard as being with the Resistance. On 13 January 1944 the Gestapo arrested Quistgaard in his home after an exchange of fire; they incarcerated him in Vestre Fængsel. His wife was not at home and managed to escape to Sweden, a fact which the resistance later communicated to Quistgaard. The January 1944 issue of De frie Danske describes a drawn out firefight around 3 pm in the Copenhagen street Aabenraa between the Gestapo and Danish patriots. The newspaper learned that five people were arrested in a building there, after they ran out of ammunition. On 28 January 1944 the Gestapo arrested Quistgaard's mother. The interrogation by the Gestapo took place at their headquarters in Dagmarhus. Quistgaard's prisondiary and letters to his wife and mother suggest that he did not feel he was subjected to torture, but rather that there was some element of mutual respect between him and his interrogators. Quistgaard's initial interrogation included sleep deprivation, including one 28-hour interrogation, and thinly veiled threats of being beaten with a rubber baton. This changed one day when his interrogator proclaimed: "It is up to you alone how long this woman has to remain here", after which the woman was revealed to be his mother. His mother was released after about two weeks of imprisonment. On 2 March 1944 Quistgaard was moved with eight others to Schwerin. On 25 April 1944 he was transferred back to Vestre Fængsel. On 12 May 1944 Quistgaard was put on trial as one of twelve members of the resistance in front of three judges from the SS. As witnesses, the prosecution presented two SOE operatives, known as Jacob Jensen and Bent. The former incriminated eight of the twelve to the point where they admitted to the charges. Quistgaard along with two other men and Monica Wichfeld were condemned to death with the execution pending any new acts of sabotage. Two days later the four death sentences were published in the Danish newspapers. On the evening of 20 May 1944 Quistgaard wrote what was to be his last letter, to his mother. It was smuggled out the following day by Jørgen Kieler. On 20 or 21 May 1944 Quistgaard and the two other men condemned at the trial were executed. Monica Wichfeld had her sentence commuted to life imprisonment but died in German captivity before the end of the war. The news of the execution was published by the papers on 23 May.
Together with Erik Briand Clausen and two other resistance members who fell victim to the German occupation Quistgaard is commemorated with a memorial stone on Gyldenløves Høj.
