Here’s a novel way of identifying the erstwhile contents of an ancient pottery vessel: never mind the chemical composition of the residue, the lipids, the proteins, the isotope ratios, the pollen, the phytholiths, the seeds or the leaf fragments. Just scrape some gunk off the inside of the sherds and check it for DNA snippets to identify the organisms that produced it!
The beauty of this approach is that you will easily see if the DNA you’ve grabbed is likely to belong to the substance originally kept in the vessel. If you come up with your own DNA or that of a soil microbe or earthworm, then you know you’ve got it wrong. There’s a book-length 1994 study by Biers et al. of perfume vials from classical antiquity where gas chromatography was used to identify the chemical composition of residues in the hope of matching perfume recipes preserved in written sources. This study was plagued by sample contamination: among the identified compounds, caffeine and nicotine made it clear that certain post-Columbian museum curators had been sloppy around their collections.
Anybody wanna buy a few amphorae of oregano-seasoned olive oil? It’s just in from Crete. For you, my friend, special price.