Scientists at Bletchley Park in southern England, the WWII code breaking headquarters, fired up the valves, whirring wheels and spinning tors of the two machines to recreate how German military chiefs sent secret messages and how they were deciphered.
Hitler's Lorenz machine boasted 1.6 million billion possible coding combinations thanks to a series of twelve rotors, a million times more complex than the more feted Enigma machine.
Through luck and the ingenuity of engineer Tommy Flowers, scientists were able to deduce how the machine operated and then build a machine to work out the settings of Lorenz's rotors.
"Colossus" is regarded as the world's first programmable, electronic digital computer, but received little attention as the project was kept secret for decades, depriving those responsible of due accolades.
Among those watching at the National Museum of Computing were Margaret Bullen, who helped build Colossus, and some of the remaining operatives who fed encrypted German messages into the machine, including Irene Dixon, now in her nineties.
It was only decades after the war that Dixon discovered she had been processing the most sensitive of information.
"We found out we were intercepting coded messages sent by Hitler to his generals," she told AFP. "Hitler would've been furious if he had known, we were decrypting the messages even before his generals were".
Information gleaned using Colossus helped the Allies confirm that Hitler mistakenly believed the D-Day landings would target Calais, and experts believe the supercomputer may have shortened the war by two years.
Dixon and other "Wrens" from the women's branch of the Royal Navy were sworn to secrecy, and even other workers at Bletchley Park were unaware of the existence of the massive computer, which took up a whole room.
"Some of the Wrens did ask why it was so hot (close to the Colossus room), and some used to dry their washing next door," recalled Dixon.
The main Lorenz cypher machine is on loan from the Norwegian Armed Forces Museum in Oslo, but the special keyboard used to send the message to the rotors is a recent discovery.
Museum researcher John Wetter saw a "telegram machine" for sale on auction site eBay and realised it was actually a Lorenz teleprinter.
He travelled to the southern English town of Southend and found the machine on the floor of a shed, covered "with rubbish".
"We said 'Thank you very much, how much was it again?' She said '£9.50', so we said 'Here's a £10 note -- keep the change," he said.
The 10 Colossus machines are believed to have been destroyed in order to maintain secrecy, but late scientist Tony Sale dedicated his life to rebuilding one as part of efforts to protect the Bletchley Park complex from
"I'm glad that my late husband's dream is being carried forward," his wife Margaret told AFP. "The last 25 years, life has been Bletchley Park. Quite a lot of people said it was an impossible task."