Contemplating something external is usually not stressful. If you do experience stress in such moments, it was likely already present—you’re just becoming aware of it because the stillness has brought it to your attention. In that case, I would go with Leo’s advice.
However, stress triggered by deep existential fear—as a direct result of contemplating the self or engaging in open, objectless awareness—is something I’ve personally felt and witnessed in others. It surprises me that Leo hasn’t experienced this. For me, it helps explain why people can go insane while meditating. I have a theory that psychosis and personality disorders are rooted in the sense of self.
After all, when you deeply contemplate the self, your very sense of being can shift drastically. It can feel like the ground is falling out from beneath you. One random association I had during meditation was that it felt like being snapped away by Thanos—like I was witnessing myself disappear.
I believe that overcoming and affirming that sense of death is one of the cornerstones of spiritual growth. Since the fear of death can be seen as the root of all fear, liberation arises as a result of facing it.
You should be cautious when experiencing stress during meditation. At worst, it could be dangerous or lead to an aversion to the practice. On the other hand, stress and anxiety during meditation can be signs of genuine progress—evidence that you're actively confronting your own death.
When this happens, try to observe changes in your breath. Since learning about and practicing Buteyko, I’ve come to believe that all forms of stress manifest as increased breath volume. The brain induces the stress response through the breath by increasing the volume of exhaled air, thereby lowering CO₂ levels in the body. The goal, then, is to counteract this by acively calming and reducing your breath.