The topic of natural aromatase inhibition came up recently in a Ray Peat interview discussing breast cancer research. Aromatase is an enzyme manufactured in the body that converts androgens, such as testosterone, into estrogens, thereby increasing overall estrogen levels. In that context, aromatase can contribute to an estrogen excess, or, "estrogen dominance", especially if progesterone levels are deficient.
As mentioned in the interview, there are many natural substances that can inhibit aromatase activity. For example, naringenin, found in orange and guava juice, and orange peel, and apigenin, found in celery and parsley, are potent anti-aromatase substances. Other anti-aromatase foods include white button mushrooms and the tea leaf, Camellia sinensis, commonly consumed as green or black tea.
Aspirin was also mentioned as an effective aromatase inhibitor.
References
Friday Night Talk, KMUD Radio Audio Archive, March 20, 2015:
http://kmud.org/programs-mainmenu-11/kmud-audio-archive.html
http://www.ncbi.nlm.nih.gov/pubmed/17178902
http://www.ncbi.nlm.nih.gov/pubmed/11739882
http://www.ncbi.nlm.nih.gov/pubmed/23370353
http://www.ncbi.nlm.nih.gov/pubmed/19127721
http://www.ncbi.nlm.nih.gov/pubmed/20669045
