How fares Lilliput in Brobdingnag? That is, how do small embassies operate in Washington? Are their ambassadors, pinstriped against the oncoming canap,es, like those other powerful fellows residing in spiny concrete palaces? What do the emissaries from the smaller countries do all day, anyway?

You might well ask.

"I attend many important functions," says the ambassador from Antigua and Barbuda, which maintains one of the smallest embassies in Washington, consisting of His Excellency and a secretary.

Barbados has a somewhat larger embassy, if a bit less diplomacy. "I'm afraid the ambassador's presently in Barbados," says a spokesman for His Excellency Extraordinary and Plenipotentiary, referring to the caller as, "Mister Whoever-You-Are."

These ambassadors to the United States do seem hard to find. The ambassador from Nauru does whatever he does in Melbourne, Australia. The ambassador to the United States from the Kingdom of Tonga has the very good taste to live in London. The ambassador to the United States from Tuvalu resides permanently in . . . Tuvalu!

How about Upper Volta?

"Ha!" shouts the secretary to that country's ambassador. "Why you pick Upper Volta?" Because it has only three representatives in the United States. "You must talk to cultural attach,e. Speak very slowly." The cultural attach,e of Upper Volta, however, doesn't like the idea of a reporter hanging about. "Right now we are having renovations."

Liechtenstein?

"We handle all the affairs of Liechtenstein," says a member of the Swiss Embassy, a bit of cultural paternalism to which our very own State Department is not immune.

"Belize!" suggests a member of State's Central American desk. "Why don't you do Belize?" But unfortunately the ambassador from Belize is also the financial secretary of Belize and is presently working on the budget in . . . yes, that's right, in Belize.

All of which brings us eventually to the doorstep of a townhouse on R Street, on the wrong side of Dupont Circle. A bulletproof glass box enables the receptionist to check out visitors before admitting them to the embassy of Singapore. On the wall hangs a photograph of the prime minister and his wife.

The name, Punch Coomaraswamy, echos through the halls with sibilant regularity. Punch Coomaraswamy is the ambassador himself, a slight 56-year-old former speaker of lthe Singapore parliament who wears the requisite pin stripes, glasses with serious black rims and an air of unfaltering discretion.

"The key thing is to get a feeling for the political scene," says Ambassador Coomaraswamy, of his duties. He uses two hoary devices-- exchanging views and gathering information.

On this particular morning he begins gathering information at 6:30 by reading the newspaper in his home, owned and furnished by the Republic of Singapore. Then he is driven in a pale yellow Mercedes 280E, belonging to the Republic of Singapore, to the Supreme Court cafeteria --"an excellent place for breakfast, by the way"-- where he obtains information from a former Democratic congressional aide about Democratic candidates for the presidency of the United States.

"I didn't want to get information from an insider's insider," he says. "I wanted an informed, dispassionate observer."

The objective is to determine who might be our next president and what that might mean for Singapore, an island at the foot of Malaysia where 2.5 million people live within a mere 235 square miles, and many Asiadollars rest in resplendent new skyscrapers.

After breakfast, the ambassador is driven to the embassy, where he reads the cables arriving from Singapore during the night. He obtains information from The New York Times and The Wall Street Journal.

Now his driver takes the ambassador, his minister- counselor and his first secretaries for politics and economics to the Thai embassy for a meeting of the Association of Southeast Asian Nations (ASEAN). They are joined by representatives of Thailand, Indonesia and the Philippines. Instant coffee and Coke are served, along with the sugary Thai pastry called golden hair, while information gathered that morning from the newspapers is discussed and views exchanged.

The representatives are concerned with the economic doldrums in the United States. Singapore exports almost everything from clothing to stereos to the United States, and an exchange of goods, as well as views, with American consumers is of the utmost importance to the ambassador from Singapore.

After the meeting, he returns to the embassy to read his mail then goes to lunch at Le Jardin, a West End restaurant where he is well known.

"Hi, Punch," call out several men at the bar, all editors for U.S. News and World Report. "How you doin', Punch?" asks the waitress, handing him a menu and taking his order for a bloody Mary.

His Excellency the Ambassador is obviously uncomfortable with all this American familiarity.

The United States has had a consul in Singapore since 1840. According to Coomaraswamy, the first consul was Paul Revere's son-in-law. Formerly a British colony, Singapore has a population that is 78 percent Chinese, 15 percent Malay- Indonesian and seven percent Indian; it has been called the proving ground for a new Asia dedicated to the free enterprise system.

"In the old days," he says, "an ambassador's concern was politics and defense. Now it's commerce and trade policy."

He has been an ambassador for 14 years, to Australia and India before the United States. He says he misses his two grown children in Singpore, whom he sees less than once a year. There is nothing frivolous about the ambassador; nothing is wasteddin the punctilious pursuit of information and exchanged views:

"Washington is the busiest diplomatic posting on earth . . . In most countries an ambassador gets all his information from a ministry of foreign affairs. Here we have, in addition to State, the Congress, the Pentagon, the National Security Council. To get the attention of these institutions, an ambassador from a small country must rely on the force of his personality."

After lunch, the ambassador is driven to the State Department for a meeting with a director of one of the Asian desks. He is most punctilious in scheduling meetings. "I'm a great believer in not pitching your level too high. I don't demand to see the secretary if what I have to discuss is not appropriate. If I don't have something to warrant an officer's attention, then the next meeting will be more difficult to arrange."

After the meeting at State, a reporter asks the ambassador what was accomplished.

"We had an exchange of views."

The driver takes him to his home, on a cul-de-sac off Foxhall Road. A metal awning extends from the front door to the street. The door is opened by a butler in a black suit, and the ambassador goes upstairs to change clothes for a reception for visiting Japanese Prime Minister Yasuhiro Nakasone at the Mayflower Hotel.

He and his wife, Kaila, a pleasant woman in a sari, come down for drinks before going out again. The parlor is furnished with Singaporean exports, including heavily lacquered tables and a pair of life-size toddlers in Chinese porcelain arranged on a rug before the hearth. An ink drawing of a reclining Buddha hangs on the wall.

The ambassador hopes to make some important contacts at the reception. "It will be impossible to go into any detailed conversation, but I may learn some things to follow up during the rest of the week. You cease thinking about receptions as something you enjoy. They are a duty."

The hotel is crowded with ambassadors, security agents and past and present American politicians. Coomaraswamy warmly greets William Colby, former director of the CIA; Richard Allen, former national security adviser, and U. Alexis Johnson, former ambassador to Japan. He joins the other ASEAN ambassadors next to the podium. "The prime minister wants to shake your hand," he is told by one of Nakasone's operatives.

"I'm being isolated," the ambassador says. "I can't speak to the people I want to speak to. There's Lyn Nofziger!"

After the prime minister speaks, he does indeed shake the ambassador's hand--and several hundred more. In the furious diplomatic swim that follows, the ambassador manages to exchange views with the former senator Frank Church and with television correspondent Bernard Kalb, who wants to buy a house in Coomaraswamy's neighborhood.

The ambassador shakes hands with Richard Armitage, the Defense Department's deputy assistant secretary for East Asian and Pacific Affairs, his most important contact.

Coomaraswamy and his wife retrieve their coats from the pile and hurry out to the waiting Mercedes. They are not done yet. The Australian deputy chief of mission, Geoffrey J. Price, expects them for a dinner in honor of the new U.S. ambassador to Indonesia, John Aldridge.

"There are no typical days in the life of an ambassador," says Coomaraswamy, on the way up Cleveland Avenue. "Some are just busier than others."

Price greets the Coomaraswamys warmly; the parlor fills with guests. Here the ambassador can neither exchange meaningful views nor obtain valuable information, but his presence is essential for maintaining good will and valuable acquaintanceships.

To an observer, the exercise seems largely inconsequential. Occasionally it seems that way to participants.

"In other countries," says a member of a middling embassy who was not invited to the Australian compound, "you attend functions with diplomats to learn things you cannot learn through other channels. But in Washington, everything is available. Unless the ambassador from England, France, Germany or the Soviet Union, or a ranking State department official, is invited to a function, that function is useless."

Ambassador Coomaraswamy would disagree. "An ambassador is needed to keep relations good between his country and the United States."

He sees the reporter to the door. The ambassador him- self hopes to be home before midnight.

Will he then send a cable to Singapore?

"Oh, no," he says. "No cable today."