Let $X \to S$ be a morphism. In the valuative criteria for properness, is it enough to test morphisms $\text SpecK \to X$ from spectra of fields to $X$ such that the image is a closed point of $X$?
This needs some extra hypothesis (because, for example, it is possible that $X$ has no closed points at all...), but feel free to assume anything reasonable. A good start will be the case where $S$ itself a field.