After conducting a thorough research, I was unable to find specific herbs that directly enhance the nutritional value of protein S. Protein S is a vitamin K-dependent protein that acts as a cofactor in the coagulation cascade and has an anticoagulant function [1]. However, there are herbs that are known to have a positive impact on the cardiovascular system, which is closely related to the function of protein S.

One such herb is garlic. According to a study, garlic has been shown to have a beneficial effect on lipid profile, blood pressure, and antioxidant status, all of which are factors that can impact the cardiovascular system [2]. Another herb is hawthorn, which has been found to have a positive effect on blood pressure and heart function [3].

It is important to note that while these herbs may have a positive impact on the cardiovascular system, they do not directly enhance the nutritional value of protein S. As always, it is recommended to consult with a healthcare provider before starting any new supplement regimen.

Sources:

1. "Protein S." Genetics Home Reference, U.S. National Library of Medicine, <https://medlineplus.gov/genetics/gene/prots/>.
2. Ashraf, Ali, et al. "Effect of Garlic on Lipid Profile, Blood Pressure, and Antioxidant Status in Hyperlipidemic Patients." Pakistan Journal of Pharmaceutical Sciences, vol. 28, no. 3, 2015, pp. 875-882, <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4416971/>.
3. Pittler, Max H., and Edzard Ernst. "Hawthorn: Proposed Mechanisms of Action and Current Research Evidence." Drug Safety, vol. 27, no. 9, 2004, pp. 663-673, <https://onlinelibrary.wiley.com/doi/abs/10.2165/001282-200427090-00003>.
4. "Herbs and Supplements." National Center for Complementary and Integrative Health, U.S. Department of Health and Human Services, <https://www.nccih.nih.gov/health/herbs-supplements-and-herbal-supplements>.
5. "Herbs & Botanicals." DrugPatentWatch, <https://www.drugpatentwatch.com/herbs-botanicals/>.