The plot of the novel hinges on the actions of a technical journalist, Keith Stewart, whose life has been focused on the design and engineering of scale-model machinery. Stewart writes serial articles about how to create scale models in a magazine called the Miniature Mechanic, which are extremely well regarded in the modelling community--as is he. He is called upon to hide a metal box in his sister's and brother in law's boat just before they plan to leave in it to emigrate to Canada. Until they are settled in British Columbia, their daughter, Keith's niece, is to remain with Keith and his wife. His in-laws are lost at sea in French Polynesia. After the deaths are confirmed, Keith is told, by his in-laws' solicitor, that there is almost no money in the estate, but there is evidence that Keith's brother-in-law has converted his wealth into diamonds to take with him abroad, to evade export and currency restrictions intended to prevent capital leaving Britain. Keith's guardianship of his niece is now permanent, and he becomes her trustee (hence the title), but where is her money?
Keith quickly realizes that the metal box he secreted contained the diamonds, and he starts to investigate how he may travel to retrieve it from the wreck. It is a difficult problem. Keith, while not poor, has chosen to do work he loves in place of better-paying work, and cannot afford to travel to Polynesia. He is able to call on connections in the model engineering world to deadhead his way on a flight as far as Hawaii. Finding no conventional way to get further which is within his means, he takes passage on the hand-built sailing ship of a half-Polynesian from Oregon, Jack Donelly. Somewhat to the consternation of Keith's friends, he and Jack sail off, (Keith having received a quick lesson in navigation) with little regard for paperwork.
One of the crew that took Keith to Hawaii, upon his return, worriedly approaches Keith's editor. The editor, somewhat shocked at the risks that Keith is taking, starts trolling the close-knit world of miniature mechanics for someone who could help Keith. Eventually, Mr. Solomon Hirzhorn, who controls much of the lumber of the Pacific Northwest from his home and business near Seattle, is informed, and immediately starts to move heaven and earth to help Keith. As it happens, Hirzhorn, an inexperienced modeller, has often sent somewhat foolish, but lengthy, letters asking for clarifications of Keith's modelling articles, which Keith always patiently answered. Hirzhorn arranges for the yacht of a business associate, Chuck Ferris (coincidentally, the yacht whose captain was consulted by Keith and Jack in Honolulu for advice on the proper course to Tahiti) to proceed to Tahiti to help Keith out. As it happens, Keith is in great need of that help, for he and Jack have arrived in Tahiti without any ship's papers, and the two are in danger of jail. The captain smooths over the situation, and leaves with Keith on board the yacht for the island where the wreck is located.
Keith reaches the island, meditates on the fate that has brought him so far, takes many pictures, erects a headstone--and leaves with the wreck's engine. It is no secret to us, but it is to the world around Keith, what is concealed in the oil in the engine's sump. After an amusing incident where Ferris's much-married daughter, Dawn, runs off with Jack Donelly, the yacht proceeds to Washington State, where Hirzhorn is anxious to meet the engineer he so admires. Keith spends several days visiting Hirzhorn, and is able to help him out by catching an engineering error in the contract between Hirzhorn's company and Ferris's that might have cost a couple of million dollars. Meanwhile, he arranges to have the engine shipped home--Hirzhorn arranges for a large consultancy fee to be paid to Stewart by Ferris's company and has his own company pay Stewart's airfare home.
Keith arrives home. The consultancy fee enables his wife to stop working and take care of their niece. The diamonds are "discovered" by Keith soon after the engine arrives, and proceeds from their sale enable them to take care of their niece's education and other needs. The other characters proceed on their lives happily, we are told at the end of what is probably Shute's most villain-free novel.
The novel represents a more liberal view of sexual conduct than we see in Shute's earlier books. The affair between Donelly and Dawn Ferris is accepted with amusement or resignation by most of the characters. In earlier books, such as A Town Like Alice, premarital sex was deprecated.