There are a few USDA certified organic honey producers in Hawaii, they take advantage of the large swaths of national forest which are managed with no chemicals at all.

I know this because they asked, and I went through an extensive and complicated dance routine with a certification agency to get Bee-Quick approved for their use in their Organic certified operations.  

To my knowledge, the "foraging range" issue makes it essentially impossible for any North American producer to gain such certification, but those sending honey into the USA market from elsewhere seem to have USDA-accredited certification agencies willing to overlook quite a bit. 

I think that the phrase "produced using organic methods" is about the best one can say in the USA, but the best price I ever got for honey was when I was one of a tiny number of Demeter International certified biodynamic honey producers in the 1990s and early 2000s.  "Biodynamic" entails a whole lot of nonsense practices that makes no difference to the bees, but it is one of the few cults that has kept up with the times, and freely admits to the need for varroa control.  So, come for the crazy German philosophy, but stay for the embarrassingly good profit margins.

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