The sort of [ethical] non-naturalism that I find appealing is one that bears a very close structural parallel to certain non-reductionist theories in the philosophy of mind. According to these latter views, mental properties are not identical to physical ones; mental facts are not physical facts; but mental properties are realized by instantiations of physical properties. At least in worlds relevantly close to ours, there would be no mental life without the physical stuff that constitutes it.
For purposes of making a comparison with the ethical realm, there are three important features of this type of non-reductionist approach in the philosophy of mind: (1) it captures our convictions about the non-identity of mental and physical properties; (2) it is not ontologically extravagant; (3) it emphasizes a supervenience relation that obtains between the mental and the physical. Each of these three features has a natural correlate in the moral domain.
Russ Shafer-Landau, Moral Realism: A Defence