Prince Charles has spoken of the "extraordinary bond" between the UK and India as his official tour got under way.
The beauty queen said it was a "once in a lifetime" meeting
He told an audience at an organisation for Indians who have studied in Britain that the ties between the two countries were longstanding.
Trade between the two had increased by 16% in the first six months of the year, he said in a speech at the Association of British Scholars.
He was speaking on Wednesday after he began his nine-day visit to India by returning to a palace he last visited 11 years ago with Princess Diana.
He was welcomed to the country with a reception at President Abdul Kalam's palace which was once the home of the British viceroy.
Later he met an Indian beauty queen when he stopped at the Tibetan community of Majnu Ka Tilla.
Miss India International Shonali Nagrani, 22, described her meeting with the "very charming" Prince Charles as "once in a lifetime", telling reporters she had a soft spot for father and son.
"I wish his sons were here - I look at William and I get goosebumps.
Prince Charles last visited India in 1992
"Most Indian women do," she said.
She spoke after she posed for photographs with Charles
alongside 20-year-old Miss Tibet Tsering Kyi.
Earlier at the Association of British Scholars, the prince described the unique relationship between the UK and India.
"This extraordinary bond has deep historic roots but is acutely modern in many of its manifestations and that modern relationship is driven by a healthy and shared perception that both countries have a lot to gain by building it further", he said.
Other highlights of the day included a five-minute train ride on Delhi's new Metro system.
Once completed, the project, helped by British consultants, will be one of the world's largest urban transport systems.
Prince Charles also visited an Asian youth entrepreneurship and employment summit run by a youth project he set up on his last visit to India in 1992.
The Bharatiya Yuva Shakti Trust, which runs along the same lines as the Prince's Trust, encourages young people to escape poverty by helping them set up their own businesses.