His latest album, Raising Sand, recorded with country singer Alison Krauss, won five Grammy awards after it was released in 2007.
After the ceremony, he said he and Charles discussed the Dimbleby lecture the prince gave this week on global challenges and the environment.
Plant's distinctive mane of hair, in certain situations, continues to exert a strange fascination.
"When I played in Essakane [in Mali, home of the Festival in the Desert] about five years ago," he recalls, "we were rehearsing 'Whole Lotta Love' in this tent, and it filled up with locals who, I later found out, were mainly discussing whether I was a woman.
Jimmy Page himself was a dazzling technician with a questing, experimental spirit: even at the band's earliest shows, he was playing guitar with a bow, and incorporating a small Theremin to broaden the sonic palette with outlandish electronic effects.
I vividly recall seeing the band in its infancy at Nottingham's Boat Club, where, despite packing as many decibels as groups like Earth (later Black Sabbath) and Free, the massive riff-driven songs boasted a superior finesse and subtlety which has rarely been equalled by later generations of heavy rockers.
Indeed, when Plant went to see his former Led Zeppelin bandmate John Paul Jones's new rock supergroup Them Crooked Vultures at the Royal Albert Hall a few months back, he admits his ears "bled for two days" after the sonic assault.
"But I feel so far away from heavy rock now," he reflects.
Although his countenance is more gnarled than in his youth, he yet commands the kind of rough-hewn appeal that doubtless still charms the pants off ladies half his age.
Plant became notorious during the 1970s for his wild behaviour.
During the band's stays at the Hyatt House hotel on Hollywood's Sunset Strip, it was nicknamed the Riot House.
'The diversity of people who have moved through here this morning prove there is no real establishment here,' he said.
Plant's date at the palace came after Paul Mc Cartney, Mick Jagger, Elton John and Cliff Richard all received knighthoods.