The tale of the customer who sent a magnum of 1961 Pétrus back because the cork did not carry the stamp of authenticity he was looking for sheds light on the new enthusiasm among the super-rich for objects of desire.

The word "trophy" has attached itself adjectivally to all manner of things. The current issue of Vogue, for example, informs us of the return of the "trophy jacket", prized because of its identifiable characteristics.

Trophies are the thing among the shockingly well off. It is not just wine that is following this pattern: certain cigars, watches and artworks have been climbing skyward. Cigars have long been a badge of plutocracy, but today it is specific cigars that appeal to the impregnably wealthy.

Any old Cuban will not do, nor is it just enough to be smoking a Cohiba, the brand once favoured by Castro himself. It has to be Cohiba Behike, a cigar made in strictly limited quantities to celebrate the 40th anniversary of the marque: 100 humidors of 40 cigars at €15,000 (£11,000), or €375 a stick. They were all pre-sold before they even made it on to the market.

These are cigars so rare that there are collectors willing to pay any sum, but it is unlikely that any will ever be resold, let alone smoked. These are cigars to keep. No more will be made. The really rich are concerned that the stuff that marks them out as individuals of substance and discrimination is, like so many of the planet's resources, running out. You can almost hear the thought process: "Well you never know, better get in early, beat the rush, just in case."

There is an element of scalp-hunting about the whole process of what is known as pinpoint purchasing. As with blood sports, it is as much about the thrill of the chase – tracking down the bottle of wine, wristwatch or cigar – as it is about owning it.

At the very top level, the problem lies not in selling trophies, but rationing them. The most sought-after Patek Philippe watches, such as minute repeaters, which chime out the hours, are difficult to make in anything other than small numbers. However, such is the demand that potential purchasers have to be vetted before they are allowed to join the waiting list.

The vintage Rolex market has also taken off but, again, not just any Rolex will do. You want a Paul Newman Daytona, a Steve McQueen Explorer, a Comex or a Double Red, even if you do not know what they are and what they do. These are out-of-production watches, originally costing a few hundred pounds, that were made in small numbers or did not sell particularly well. Now they fetch tens of thousands of pounds. Often it is only forensic details that give these watches trophy status: the colour of the printing on the dial, the serif on a number or letter – but it is enough.

Daniele Pizzigoni, who deals in such timepieces from his shop just off Bond Street, remembers one customer who handed over his credit card and told Mr Pizzigoni to charge what he wanted for such a trophy.

These items – and even the boxes for vintage Rolexes, another object of mega-rich aspiration – exist only in finite numbers. Yet some are vanishing fast. The upmarket wine merchant Corney & Barrow insists that every bottle of Pétrus it sells is destroyed once its contents have been consumed.