Before Rome, the singer was in the actor's native Suffolk on the east coast of England to meet his mother
The pair, who met May 1 at the Met Gala, flew into Rome on the pop-star’s private jet and landed at Ciampino airport on Monday, for a day of sightseeing (and kissing!) around the Eternal City.
Their first stop in the morning was the historic Colosseum at the Italian capital, where the singer, 26, and her actor beau, 35, were spotted holding hands during their private tour of the grounds accompanied by four bodyguards, a director from the administration and an English-speaking art-historian.
A Colosseum source told PEOPLE the tour lasted 45 minutes and the pair posed many questions to the art historian – particularly interested in all the mechanisms devised by the Romans to create/allow the special effects that took place during the events (like lions and other wild animals appearing from nowhere thanks to elaborate and hidden manhole mechanisms).
The insider says that at one point, the art historian pointed out how the events held there were the most popular type of entertainment in those days – just like one of Swift’s concerts today. The comment prompted the pair to laugh, the source says.
Despite skipping the queue due to their private tour booking, the VIPs were made to pass through the security metal detectors like any other tourist. That proved to be a challenge, the source says, as one of the bodyguards was armed and need special clearance to enter the site.
After the Colosseum, the pair walked briefly across to the Roman Forums located a few meters away. Again the guide provided a detailed explanation of the history of the Roman ruins.
Following their tours, the rumored couple were pictured dining at a nearby restaurant together, where Hiddleston sweetly kissed Swift’s hand.
News of their visit spread across the Italian capital, prompting hoards of teenage fans to gather in front of the door of the 5-star Hotel de Russie, where the couple is staying on the fifth floor’s luxurious suite. Groups of girls took turns to serenade the singer with her own hits like “Love Story” and “I Knew You Were Trouble.”
Actor Dan Levy, of Pop’s Schitt’s Creek, documented the gathering on Instagram, saying, “Taylor Swift is staying at my hotel. These teens have been singing her songs outside all day/night. Suuuuper chill vibes.”
Some fans stalked the entrance for hours in a bid to see Swift and were rewarded only later in the evening when the pair returned to their accommodation in a black chauffeur-driven Mercedes.
This Italian excursion comes just days after Swift met the Night Manager star’s mother Diana in his native Suffolk on the east coast of England.
And their romance appears to be moving very swiftly.
The same weekend she met Diana, Swift introduced Hiddleston to her parents Scott and Andrea at her Nashville, Tennessee apartment. The 1989 hitmaker has also introduced her new man to many of her friends in Nashville, including childhood BFF Abigail Anderson and country singer Kelsea Ballerini.
Swift and Hiddleston’s romance has been highly publicized especially after they were pictured kissing in Rhode Island earlier this month.