Michael D Higgins is halfway through a four-day state visit, which includes the Northern Ireland-themed reception hosted by the Royals.
More than 200 guests from the worlds of politics, business and sport were invited for the event which recognised those who have contributed to building positive links between Britain and Ireland.
First Minister Peter Robinson of the DUP and Mr McGuinness were introduced to Her Majesty and the Duke of Edinburgh as they arrived, alongside other local MPs and MEPs from across the spectrum and NI Secretary of State Theresa Villiers.
Mr McGuinness - who previously shook the Queen's hand and toasted her while standing to the UK's National Anthem - said this week's historic state visit will be remembered for its "spirit of generosity and peace-making".
The former IRA commander continued: "She had many reasons not to meet me, and me her, but I think we've risen above that and seen the contribution that these big acts of reconciliation can have.
"I'm overjoyed for the president. He is my president and I'm delighted he's been accorded such a great welcome."
Mr Robinson said: "We have to build upon respecting each other's traditions - sadly sometimes lacking - but if you see that Her Majesty has been willing to invite Martin McGuinness, and Martin McGuinness agreeing to come, all demonstrates that there is a new era of respect and tolerance.
In terms of the north and the south, we've had the best relationship with the Irish government we've ever had in our history.
"We're pushing in the same direction to get peace and stability that is well grounded."
Earlier, Sinn Féin Belfast Lord Mayor Máirtín Ó Muilleoir said he was "honoured" to take part in the event alongside the Lord Mayor of Dublin Oisín Quinn - a first for a Lord Mayor from his party.
"It is an honour to be included in this ground-breaking and historic visit aimed both at bringing the people in our two islands closer together and fostering reconciliation at home," he said.
"Along with the Lord Mayor of Dublin, I am keen to promote that message of reconciliation and show respect for the unionist tradition in Belfast and beyond. Despite the challenges this presents to me personally, I am determined to deliver on my pledge to be a Lord Mayor for all."
Some of Northern Ireland's greatest sportspeople were also present for the evening.
Paralympic skier Kelly Gallagher, who recently won gold in Sochi, handed her medal to the Queen after she asked to see it.
The Bangor athlete said: "The Queen asked me if she could hold the medal. She said that when her grand-daughter Zara won a medal, she wanted to show it to the whole world.
"It's amazing to be at an event like this and to be able to celebrate sport."
Mary Peters, an Olympic gold medallist from 1972 and now the Lord Lieutenant of Belfast - making her the Queen's representative in the city, described the state visit as "sensational".
She said: "It's been such a great journey for me as a sportsperson to be able to be in such august company. I regularly meet Prince Philip and the Queen when they are in Ireland. Somebody asked the Duke of Edinburgh if he knew me and he joked: 'Yes, I've known her since she was a little girl'."
The reception at Windsor Castle was followed by the Ceiliúradh - a celebration of Irish culture - in the Royal Albert Hall on Thursday evening, where President Higgins and his wife Sabina were joined by Prince and Princess Michael of Kent for a concert of music, spoken word and dance.
A further speech was delivered there by the President of Ireland.
He said: "This evening's celebration demonstrates once again the importance of culture in general and, in particular, the depth and richness of our Irish cultural tradition.
"What we have seen and heard also shows how deeply interwoven are the wider cultures of these islands, and how they have influenced and enriched each other."