Two typhoon jets armed with air-to-air missiles intercepted the Prime Minister's plane as it returned to the UK from Cyprus.
The fighter jets pulled up alongside the RAF Voyager, flying at 17,000 feet, before tipping their wings as part of a training exercise for a suspected hijacking or mid-air threat scenario.
The Prime Minister watched from the cockpit as the pilots from 3 Squadron and 11 Squadron performed the manoeuvre.
The typhoons, scrambled from RAF Coningsby in Lincolnshire, also hooked up to the Voyager for air-to-air refuelling, each taking on four tonnes of fuel during the exercise at 600kg a minute.
The PM said "I'm delighted to have the opportunity today to see our brave pilots and crew in action refuelling in the air to prepare to fight Daesh in Syria and Iraq."
She said: "Witnessing the unique skill of the RAF at first hand is an absolute privilege and demonstrates that the British Armed Forces are the finest in the world.
"The work they do is admirable and impressive and I want to take this opportunity to thank them for everything they do to keep us safe."
The demo marked the end of Mrs May's two day trip to Poland and Cyprus, the Prime Minister's last foreign visits before the New Year.
Mrs May spent the return journey working on papers from her ministerial Red Box and relaxed with a sudoku number puzzle.
The Prime Minister was returning from RAF Akrotiri where she praised the sacrifice of personnel involved in operations against Islamic State.
Theresa May arrived at the air base late last night and was today shown around the 14 RAF jets flying operations against IS. She then met with personnel involved in OP Shader and military families based in Cyprus.
Mrs May met with engineers, armourers and technicians working on Typhoon and Tornado GR4s, as well as aircrew who fly missions over Iraq and Syria.
During a speech this morning, Mrs May told a gathering of servicemen and women that the nation was grateful for their efforts to keep the country safe and bring stability to the region.
Op Shader, the UK’s contribution to the war on IS, has involved RAF jets and Reaper drones launching more than 1600 airstrikes on IS since operations began in September 2014.