BigThink has a research article on the health benefits of Self-Compassion meditation.

Which brings us to a new study, conducted at the Universities of Exeter and Oxford and published in the journal Clinical Psychological Science on February 6. The research team assigned two short-term self-compassion exercises to 135 participants alongside control conditions that involved negative, neutral, and positive valences. The results: people feel better, physically and mentally, when they practice kindness.

Specifically, when practicing self-compassion, the volunteers experienced reduced arousal — heart rate and skin conductance, increased parasympathetic activation, heart rate variability, etc. Their nervous systems responded better when their mindset invoked kindness instead of excitability and agitation. It's an interesting finding, however "the underlying processes for this," as the researchers explicitly state, are still "not well understood."