The nuance of '媚びる' is tricky to capture in a single English word, but 'to fawn over' comes closest in my experience. It carries that sense of excessive flattery or obsequious behavior to gain favor. I remember watching characters in 'The Crown' fawning over royalty with exaggerated deference - it perfectly illustrated that dynamic.
Another option is 'to grovel,' though it leans more toward humiliation. When a character in 'Game of Thrones' groveled before Cersei, it wasn't just flattery but desperate submission. The Japanese term can sometimes imply more subtle social maneuvering than outright groveling though.
'To curry favor' works well for workplace contexts where someone might excessively compliment a boss. I've seen this in office dramas where junior employees strategically praise superiors while hiding their true opinions - that calculated social dance feels very '媚びる' to me.