British bookies Ladbrokes were offering 100-1 for either Charlene Riva or Myla Rose to win the grasscourt title just a day after Federer's wife Mirka, 31, gave birth to the tots.
The twins, whose Swiss father has won a record 15 grand slam titles, were also 25-1 to claim one of the four slams with all bets based on either doing so before their 25th birthdays.
The girls, who were born at a private clinic in doubles team and 200-1 to take the Wimbledon doubles crown.on Thursday, are 50-1 to win a grand slam as part of the same
"The twins certainly come from good tennis stock. If they are half as good as their dad they will still be a potent force on the court," said Ladbrokes spokesman Nick Weinberg.
American Andy Roddick, who the 27-year-old Federer beat in last month's Wimbledon final to claim his 15th grand slam, sent a message from his Twitter page about the twins.
It read: "Wimbledon women's champs in 2029-2040 .... the Federer girls: congrats to the new parents!"