The lesbian mothers of IVF twin girls have lost a legal bid to sue their doctor for the cost of raising one of the toddlers.

The women, whose names have been suppressed, sued prominent Canberra obstetrician Sydney Robert Armellin for more than $400,000 for implanting two embryos instead of the requested one.

The ACT Supreme Court today ruled in favour of Dr Armellin, and ordered the couple pay his legal costs.

The IVF procedure, which used sperm from a Danish donor, resulted in the birth of twin girls, now aged four.

The couple, whose combined income is more than $100,000, sought $398,000 from Dr Armellin to cover the costs of raising one of the girls, including fees for a private Steiner school in Melbourne.