Simon, our Maasai guide, pointed the 4x4 towards the river and we bumped our way across a great swathe of savannah. We gave only a cursory glance to a bachelor herd of bolshie-looking buffalo, and paused only briefly to admire a pride of well-fed lions, sleeping in various states of abandon. Once we had reached the banks of the river we slowed and anxiously scanned every rock, tree and hollow.
My husband, Ludo, and I knew that we were finally in with a real chance to glimpse an animal that had always eluded us in the wild. We just had to be patient.
My eye caught something: a patch of colour against the grass. "Stop!" I called, and raised my binoculars. Dark eyes looked back at me, large ears twitching away the late afternoon insects. A reedbuck, an elegant animal with a rich russet-red coat; lovely, but not what we were looking for.
An hour later it seemed we had scrutinised every inch of the riverbank, to no avail.
"She might have moved away, but she won't go far. Let's try up there," said Simon, and he pointed the vehicle towards a thicket of low bushes. We circled it once, twice, eyes straining to pick out anything among the dense vegetation. Nothing.
Daylight was beginning to ebb away, along with my hopes. We circled again, every sense alert to any sound or movement. "There she is!" A triumphant Simon pointed at a blurred outline camouflaged among the leaves. We raised our binoculars and great big grins spread across our faces. A leopard. And, her cub.
Kenya is justifiably renowned for its wildlife and for many years it was top of the pops as far as big game viewing was concerned. Now, though, the national parks seem to have almost as many 4x4s as antelope, all tuned into each other's radio frequencies and racing in formation across the savannah when someone broadcasts that they've spotted a lion. The poor beast is then swiftly encircled by several dozen vehicles full of the zooming lenses and clicking cameras of furiously competing tourists.
The process isn't great for the wildlife or for the people who have made the journey to come and see it. And tens of thousands of them do, all needing to be flown in, driven about, fed, watered, showered, pampered and given somewhere to sleep. The natural resources of the national parks, set up to protect animals and their habitat, are therefore coming under increasing pressure in order to service the needs of a constant stream of human visitors.
Wildlife tourism accounts for a healthy slice of Kenya's gross domestic product and that, in turn, puts a high value on the country's wild animals, making their conservation a matter of national importance. That's all good news, but not if it becomes unsustainable and starts to destroy the very places people flock to Kenya to see.
Some conservationists and companies specialising in wildlife tourism already fear that the pressure on the national parks, particularly in the peak seasons, is unsustainable. They are looking beyond the boundaries of the parks to neighbouring tracts of land, which they believe can be managed and run to benefit wildlife, tourism and the local community.
Known as "conservancies", some have already been established, most notably Lewa near Mount Kenya. And we arrived in time to celebrate the inauguration of a new one called Naboisho: 20,000 hectares on the edge of the Maasai Mara reserve. A consortium including Norwegian champions of environmentally-conscious tourism, Basecamp, have rented the land from the 500 Maasai families who own it, guaranteeing them an income for the next 15 years.
There will be beds for just 140 people, ensuring low density, low impact tourism and no unruly crowds of four-wheel-drive vehicles. Basecamp has an award-wining lodge on the edge of the Maasai Mara Reserve, and we spent three days there game viewing.
It was here that we saw our leopard, as well as elephants, buffalos, lions and hyenas. But it was also the season when everything was giving birth: the grasslands were full of miniature zebras, wildebeest, gazelles and giraffes. Would the conservancy, still occupied by Maasai families and their animals, be able to compete?
We stayed in Basecamp's mobile camp, set up in a beautifully wild spot among acacia trees. A fire was kept burning all night and two Maasai askaris (soldiers) kept guard – not to keep people away, but to deter the lions and hyenas we heard roaring and whooping in the darkness beyond.
At dawn we set out and very soon came across the big grazing herds: towering giraffes, prowling lions. We scattered a group of banded mongooses, and spotted a family of bat-eared foxes, the young cubs peeping out from the mouth of their den. At the remains of a kill, a clan of hyenas squabbled over the bones under the watchful gaze of five different species of vulture.
A herd of Thomson's gazelles racing full-pelt cross the plain alerted Ludo: "Cheetah!" And we watched as this most elegant of cats missed its quarry and returned to the shade of a tree accompanied by the mocking cackle of guinea fowl. The only thing we didn't see was another vehicle. It was as if we had the entire place to ourselves.
The notion of sustainability seems to be catching on here. Even Safarilink, the airline which flew us to the airstrip, offsets its carbon by supporting a tree-planting project and donates a percentage of the ticket price to conservation, a sign, perhaps, that Kenya understands the need for a sustainable future.
We took the same airline down to the Kenyan coast and over to the island of Lamu. I hadn't been there for over a decade and was intrigued, and a little fearful, of how it might have changed. Lamu Town, with its narrow maze of streets and bustling market was, refreshingly, little-altered. However, around it on both sides are a number of new, swanky hotels and glitzy private houses.
The Red Pepper House is the indescribably elaborate home of a Spanish interior design mogul. It's run as an exclusive boutique hotel – it has just five rooms – when he's not in residence. Set amid four hectares of leafy garden, with a pool, hugely attentive staff and a chef who can whisk up everything from chocolate croissants to sushi, it is the height of extravagant luxury, with a price-tag to match.
At the other end of the island, things were very much the same as they had been when I'd last visited. Here Mary-Jo Van Aardt and her family have established a haven for worn-out visitors who, like me, have forgotten to pack anything other than walking boots and flip-flops.
Kizingo is a little hamlet of bandas strung out along the beach. All built of local materials, with no glass in the windows and no doors. They are light, airy and naturally cooled by the breeze off the sea. Crabs scuttle along the beach, seabirds dive for fish, fishermen wave from their dhows.
Over dinner (the ingredients for which were supplied by the local fishermen and Kizingo's vegetable garden) Mary-Jo's husband, Louis, told me about the coastal bottle-nose dolphins that are regularly seen just beyond the island's tip.
Their daughter Emily took Ludo and me to look for them the following morning. Soon after setting off we spotted something at the surface; not dolphins but two green turtles. These lay their eggs on the beach just beyond Kizingo and Mary-Jo's family plays an active part in the local turtle conservation project. Soon afterwards I saw four dorsal fins break the surface of the sea. We scrambled for our fins and masks and were rewarded with a brief but exhilarating view of the dolphins diving. With a casual flick of their tails, they disappeared into the blue.
"They were hunting, I think," said Emily. "Sometimes they stick around for a bit, but they seemed to be on a mission."
Back in the boat we pressed on, then just a few minutes later Emily spotted another group of six dolphins swimming in tight formation right at the surface. We slipped back into the sea and swam gently away from the boat. As we floated, the dolphins swam around us, diving and gliding, clicking and squeaking.
Emily dived down and they swam alongside her and then headed back up as if to encourage the rest of us to follow them too. We needed no second invitation. Here we were, in the open ocean, with a wild pod of dolphins that appeared to find us amusing enough company to want to stay around and play.
In just 10 days we'd seen a wild leopard for the first time and swum with wild dolphins. Kenya is still, undoubtedly, somewhere that should be on everyone's list if they want to see some of the world's most charismatic and spectacular species. But it is up to us, as much as the tour operators and conservationists, to make the right choices to keep it that way.
Kate Humble presents 'Lambing Live' tonight at 6.30pm on BBC2.
Travel essentials: On safari
* Kenya Airways (020-8283 1818; kenya-airways.com) flies daily from Heathrow to Nairobi with connections to Mombasa.
* Nairobi is also served from Heathrow by BA (0844 493 0787; ba.com) and Virgin Atlantic (0844 874 7747; virgin-atlantic.com).
* Monarch (0871 940 5040; monarch.co.uk) flies non-stop between Gatwick and Mombasa.
* Safarilink (flysafarilink.com) offers daily flights to all the major game parks in Kenya. Return flights from Nairobi to the Maasai Mara start at US$265 (£177). To Lamu, flights start at $365 (£243). Safarilink donates $5 for each passenger into or out of Lewa to the Lewa Wildlife Conservancy (lewa.org).
* Tribe Hotel, The Village Market, Nairobi (00 254 20 720 0000; tribe-hotel.com). Doubles start at US$320 (£213), room only.
* Basecamp Explorer (00 254 20 387 7490; basecampexplorer. com) operates Basecamp Maasai Mara (doubles from US$480/£320), Basecamp Wilderness (doubles from US$590/£393) and Basecamp Dorobo Bush Camp (doubles from US$590/£393). All rates include full board, two game drives per day and transfers from Maasai Mara airport.
* Red Pepper House, Coconut Beach, Lamu (00 254 20 251 3147; theredpepperhouse.com). Doubles start at US$1,270 (£847), full board with activities.
* Kizingo, Lamu (00 254 73 395 4770; kizingo.com). Doubles start at US$390 (£260), full board including transfers and activities.
Red tape & more information
* British visitors can buy a Kenyan visa on arrival for £20 (kenyahighcommission.net).
* Kenya Tourist Board: 020-7367 0931; magicalkenya.com