Princess Alexandra said yes to the Florence Nightingale Museum, the Duke of Edinburgh has pledged his allegiance to the National Maritime Museum and Michael Palin is committed to the Pitt Rivers Museum and Tate.

Celebrity and royal patrons are invited by organisations to raise their profile, and in some circumstances use their connections and influence - directly or indirectly - to bring in cash. The pulling power of a patron cannot be underestimated, but at the same time, cannot exactly be quantified.

Colin Tweedy, chief executive of Arts & Business, thinks royal patrons are an important part of national organisations. "They are phenomenal for raising the profile of an institution," he says.

Tweedy, who is a trustee of the Serpentine Gallery in London, says the Kensington gallery was transformed by its patron, the Princess of Wales. "She used to come to all the summer parties," he recalls. "Now it is the smartest place to be."

But how does a museum go about seeking out an appropriate celebrity and then building a relationship with them? Julian Porter, the curator of Bexhill Museum, had his eye on actor, comedian and Bexhill son, Eddie Izzard, for some time.

In the past, the museum had co-opted local dignitaries as honorary presidents, but after the restructuring in 2003, Porter wanted a higher profile for the museum. "We wanted someone better known and desperately wanted a local connection," he adds.

Izzard came on board last year and has not only suggested themes of work, such as a project about smuggling, but is also pushing for Wi-Fi facilities to be installed at the museum when it is redeveloped in 2009. Porter says the comedian has made the museum "quite a bit trendier than we would otherwise be".

Porter is unsure of the benefits a royal would bring to Bexhill, regarding it as an old-fashioned approach that could alienate younger visitors and those from diverse backgrounds. He regards Izzard as a "figurehead, giving his endorsement", and describes him as "our first member".

But he is unequivocal on the extent of the comedian's involvement. "We are not expecting him to bail us out with cash if we get into trouble," stresses Porter.

For Porter, it is about the kudos a celebrity of Izzard's standing brings. "Organisations we have dealt with take us more seriously," he says, adding that phonecalls are returned and letters responded to. "There is a little more respect. I am convinced it has an enormous effect."

John Stewart-Young, director of the McManus Galleries in Dundee, says the finances are the focus when it comes to patrons. He drew up a list of potential candidates. "All was done with the development of the McManus in mind," he says. And for the new McManus - costing about £10m - just one patron wouldn't do.

"You need the mix," adds Stewart-Young. "They all have different qualities and skills. No one person is going to be good at everything." The allure of the McManus Galleries was enough to entice media darling, Lorraine Kelly; the well-connected Lady Airlie; academics Alfred Cuschieri and Bernard King; and actor and strong advocate of Dundee's development, Brian Cox. All have ties to Dundee or the surrounding area.

Unlike Porter at Bexhill Museum, who said he was tempted to ask Izzard to do a comedy turn in the museum but realised that he should wait for the comedian to suggest it, Stewart-Young leaves shyness aside. His plans include a request for a London tour with Lady Airlie to meet some of her contacts. "You have got to be up front about it," he says.

And perhaps these methods are working. According to Arts & Business's figures for 2006-07, individuals in the UK were willing to invest £29m in museums. That is up from £22.4m in the previous year, and almost £5m more than businesses contributed to the sector in 2006-07.

Louise de Winter, director of the National Campaign for the Arts, says patrons are often the key to successful fundraising. "They need to be nurtured, as it is becoming harder to get money from the corporate purse, and big blockbusting individuals are in a league of their own - and there are only so many of them."

Tweedy adds: "Some people are nervous of it [patrons' fundraising], but there has never been enough state funding. This is the way ahead. There is no going back."

While it is difficult to know how much of the £29m is brought in by a celebrity or royal patron, it is easier to evaluate the contribution made by another type of patron. Set up as a kind of elevated form of membership, museum patron schemes offer exclusive benefits and a special relationship with the museum to individuals in return for a minimum contribution each year.

At the Victoria and Albert Museum (V&A), anyone can become a patron if they can give at least £1,000 to the museum every year. Philippa Ouvry, head of friends and patrons, says the motivation to become a patron is caring about the collections and wanting to know more about them.

"A lot want a closer relationship with the museum and want to have this on a regular basis," she says. In return, they receive invitations to openings, as well as the chance to meet the curators and to attend handling sessions of objects such as those destined for the new medieval and renaissance galleries. And, as Ouvry points out, £84 a month is little more than a gym membership.

If you are willing to part with £5,000 a year, the V&A invites you into the Director's Circle. What sounds like a secret society - it has attracted 18 people so far - is pitched as an opportunity to be increasingly involved with the museum.

In addition to the benefits offered to ordinary patrons, the privileged few can join the director of the V&A for an annual dinner held in the museum. External events, which cost extra, include educational visits abroad, such as a trip to Palermo, via Rome, in 2006.

While contributions from the general patrons go to "areas of need", Director's Circle patrons know exactly where their cash goes. It is initially placed in the director's discretionary fund, and later used for specific projects.

Russ Carr has been a patron of the V&A since 2002 and was attracted by what he calls the museum's increased awareness of accessibility. He has subsequently been impressed by the passion, enthusiasm and ideas of the curators. "I didn't become a patron just for the benefits," he says. "My donation does make a difference, perhaps contributing to the cost of late-night openings and other free events."

Carr admits that it would be nice to have the added advantages offered to members of the Director's Circle, but felt that giving money to more than one arts organisation was more of a priority for him. Jeremy Strachan was a V&A corporate patron and continued his association when he retired.

"A patron is a friend - but with a few more bob," he says. His interest in art and design as a hobby is an important reason why he has remained a patron. He is equally attracted to the giving as the benefits he receives. "I am satisfied by what I get," says Strachan. "If the balance was disturbed, I may well take my chequebook elsewhere."

The Tate's patron scheme has been running for 25 years. There are three tiers - silver (£1,000), gold (£5,000) and platinum (£10,000). Head of patrons Gemma Honniball says the draw is the collection and access to the art world.

The Tate's patrons are given particular powers to select acquisitions presented to them by curators. All the artworks are wanted by the Tate, but it is a select committee made up of seven patrons that has the final say. Each year, two-thirds of patrons' money goes towards acquisitions.

Simon Dickson, head of development at the Natural History Museum, makes the distinction: "Members are motivated by what benefits they get, patrons feel they are supporting a cause." Quite often, it is the celebrity or royal patron that attracts individuals to museum patron schemes, who in turn provide that additional impetus to the fundraising mission.