In this paper I examine a set of exceptional aesthetic experiences that remove us from our pragmatic everyday life and involve a specific type of unaffordability. I then extend this notion of unaffordability to experiences of awe and its relation to the sublime. My analysis is guided by considerations of the phenomenologically inspired enactivist approach that supports an affordance-based accounts of aesthetic experience. I review some recent neurophenomenological studies of the experience of awe, and I then sketch out a phenomenology of awe as it approaches the sublime.