Tayyab Subhani, 30, and Mohammed Safdar, 41, were detained at Stansted Airport on Friday after a Pakistan International Airlines (PIA) flight they were on had to be escorted to safety by Royal Air Force Typhoon jets over UK airspace.
The two have been charged with endangering the aircraft.
The charge against them read out at Chelmsford Magistrates' Court said the duo had made false threats that "crew and passengers would be killed and the aircraft blown up before landing which was false, misleading or deceptive".
Lawyers for the men said it was their intention to plead not guilty.
PIA Flight PK 709 from Lahore was diverted en route to its scheduled stop at Manchester Airport after the pilot sent a signal to Air Traffic Control.
The two British citizens were travelling back from Pakistan after attending Safdar's mother's funeral, the court was told.
The Boeing 777 plane, carrying 308 passengers, was shadowed into Stansted - Britain's designated counter-terrorism airport - by Royal Air Force jets after the pilot reported threats being made.
They will next appear at Chelmsford Crown Court for a plea and case management hearing.
Endangering an aircraft carries a maximum sentence of life imprisonment and their case will be dealt under the UK's Aviation Security Act 1982.
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