Episodic memory relies on constructive processes that support simulating novel future events by flexibly recombining elements of past experiences, and that can also give rise to memory errors. In recent studies, we have developed methods to characterize the cognitive and neural processes that support conscious experiences linked to this process of episodic recombination, both when people simulate novel future events and commit recombination-related memory errors. In this Perspective, we summarize recent studies that illustrate these phenomena, and discuss broader implications for characterizing the basis of conscious experiences associated with constructive memory from a cognitive neuroscience perspective.