Miss Waugh, who is originally from Durham and is unmarried, had worked in Libya as a payroll executive for up to ten years but had maintained a home in London.
She had been due to start a new job in Malta when she disappeared.
She was last seen shopping in central London on May 4 but failed to attend 50th birthday celebrations with her family in June.
Relatives said she had never gone missing before and had always called them three or four times a week.
Margaret Waugh, 78, her mother, told the Daily Telegraph: "I think the world of her and I fear she's been kidnapped, I don't know why.
"She spoke to me two or three times a week but then all of a sudden, nothing.
"After three weeks, I called my son, Chris, and when he couldn't get a response from her either we realised something was seriously wrong."
Mrs Waugh added: "She always went running at night. I gave her a device to carry, an alarm, but she never bothered with it. She said there was nothing to worry about."
Forensic experts have combed Miss Waugh's flat and detectives have sought to contact her friends and associates.
Detective Chief Inspector John McFarlane, who is leading the inquiry, said they were extremely worried about her as it was "totally out of character."
He said: "Miss Waugh is a successful businesswoman who has worked in the oil industry and in finance for a number of years.
"She is well respected by her colleagues and was in regular contact with her family until she suddenly vanished.
"I'm keeping an open mind as to what has happened to her and we are pursuing a number of lines of inquiry but I've found nothing in the last two days to reassure me at all of where she is or if she is OK."
Anyone who can identify the two women pictured, is asked to contact the police incident room on 020 8721 4205 or speak to Crimestoppers anonymously on 0800 555 111.