Ewe, Shirley showed no signs of having mated with Dave the ram and a recent ultrasound scan came back negative.
Staff at White Post Farm in Farnsfield, Nottingham, were stunned when they found her nursing the little lambs in her pen when they turned up for work.
Spokesman for the farm Anthony Moore said: “As far as we’re concerned it’s a miracle.
“There was no evidence whatsoever that the ewe had been with the ram and nothing came up on the ultrasound.
“A more sensible man may tell you it was a mistake but as far I am concerned it’s a miracle.
“The only possible suspect for the dad is a Dorset ram called Dave.
“He’s been looking very sneaky and suspicious. I’m sure the only way he could have managed it is using wires like out of Mission Impossible.
“The lambs are doing really well – a good size and mum is feeding them perfectly.
“They are a beautiful black and white colour which simply adds to the mystery as the ram and ewe are both white Dorsets.
“The farm is buzzing with new life and festive cheer at the moment and this is the icing on the cake.”
When a ram is put into a field to woo a ewe, it is fitted with a special harness that has a block of crayon fitted at chest height.
As the gent mounts the lady sheep, the crayon rubs off on her back – showing farmers that they’ve mated.
But back in July the “virgin” ewe came away from an encounter with the farm’s ram with no crayon in sight.
There was a second attempt to hook them up in October but again the ewe came away looking spotless.
A subsequent ultrasound showed no signs of pregnancy.
Site director Simon Rouse, who has worked on the farm for the last 18 years, said: “We did start to wonder if maybe she wasn’t cycling.
“Obviously it was a mistake by a scan man. It was a surprise but a happy one – and now there are two bonny and healthy twin girls.”