Perhaps emptiness cannot be experienced so much as allowed for. We can allow that it is veritable, though transcendent and inaccessible because of the very nature of mind. The picture of reality painted by modern physics is of an insubstantial world. In outer space, too, the picture is of relatively little content dispersed in vast reaches of empty space. To refer again to modern physics, the picture is that space is not empty, but itself seething with potential energy.
New particles can appear out of nothing but the energy of space.
This aspect of physical reality has its parallel in subjective experience. We can know the insubstantiality of perception and thought as mental constructs, as subjective illusion. We can know the truth of the emptiness of our concerns, and of all the movements of mind, of all thoughts including emotion. And far from being distraught because of it, we can also know the seething energy underlying this emptiness and filling the stillness of mind.