Instead, they keep a low profile, and perhaps for good reason.
Last month, the United States Treasury Department, in its bid to increase pressure on Myanmar over human rights abuses, slapped sanctions on a major conglomerate, Asia World, and 10 Singapore-based companies owned by Mr Law and his wife.
They include Golden Aaron, GA Ardmore, GA Capital, GA Foodstuffs, GA Land, GA Resort, GA Sentosa, GA Treasure, GA Whitehouse and SH Ng Trading.
Golden Aaron, which was started in 1995, clinched a deal in 2004 to explore the coast off Myanmar with the country's state-owned oil company and China's largest offshore oil and gas outfit.
Under the agreement, the three companies were to carry out oil and gas exploration in a 10,000 sq km area in Rakhine state in the south-west and a 15,534 sq km area in the gulf of Mottama off Tanintharyi in the far south.
According to the Accounting and Corporate Regulatory Authority, the company has a paid-up capital of S$5 million.
US President George W. Bush said last month that the targeted sanctions 'focus on the assets of regime members and their cronies who grow rich while Burma's people suffer under their misrule'. Burma is the former name for Myanmar.
Mr Adam Szubin, director of the Office of Foreign Assets Control (OFAC), explained to The Sunday Times that if it did not sanction those companies, 'then Steven Law could sidestep the law by placing his assets into firms owned by his wife'. OFAC is an agency of the United States Treasury Department.
Mr Law, who also goes by his Burmese name Tun Myint Naing, is the son of Mr Lo Hsing Han - dubbed the 'Godfather of Heroin' by OFAC - and one of the wealthiest individuals in Myanmar. No photographs of his wife are available, and a check with high-society magazines here, The Peak and Prestige, drew a blank.
A freelance photographer, who wanted to be known only as Wong, told The Sunday Times that many 'rich and famous folks guard their privacy jealously'.
'I seem to remember the Laws being one of such who officially requested not to have their pictures taken or published,' he said.
Even friends and acquaintances know very little about the couple. They spoke to The Sunday Times only on the understanding that they are not identified, for fear that their businesses are affected or 'sanctioned'.
One acquaintance said Ms Ng, who was born in 1958, studied at Dunman Secondary School and Hwa Chong Junior College.
A check on the Internet found that she is the third daughter of Mr Ng Ah Khoon and Madam Hong Or Tew Chua. Attempts to contact Ms Ng or her parents at their home in Jansen Road have failed. There was no one at home each time The Sunday Times paid a visit.
Ms Ng married her college sweetheart, now a second-hand car dealer, and had three children by him. She divorced him and married Mr Law in 1995.
A businesswoman who used to play mahjong with her more than 20 years ago said she was 'friendly but kept a distance when it comes to her business of private affairs'.
'A group of us used to hang out socially but I haven't seen her since 1988. People change. I heard she had moved out of the country with her new husband,' she said.
Golden Aaron's office at Shenton House was shut when The Sunday Times visited it late last month. But its doors were open on another visit last Friday. The company sign on the glass door - listing Golden Aaron Pte Ltd, Kokang Singapore Pte Ltd and S H Ng Trading - had been taken down.
An employee said Ms Ng was out of the country. She would not say where she was or how long she had been out of Singapore.
The Sunday Times also visited Ms Ng's condominium home off Alexandra Road last Friday. No one was at home except for a cleaner, who said she cleaned the unit once a week.
She said Ms Ng was in Myanmar and that she spent most of her time there on business matters, returning to Singapore every one or two months.
The last time the cleaner saw her was during the Chinese New Year.
Additional reporting by Diana Othman and Teo Cheng Wee