I'd say mainly by dealing out/emphasising those things:
- Challenges
- Fame
- Fortune
- Power
Challenges are the enemies one faces, and the stuff that is at stake. In my current high level campaign (16th), the PCs face plots that threaten to topple entire kingdoms, deal with conspiracies involving major churches and even gods, and deal diplomatically with rulers. Their enemies are of the same quality, ruling countries or churches.
Fame is the result of beating those challenges. The PCs are known, by nobles and commoners. Even outside their native land, the rulers know of them, may even keep tabs on them. In the areas they were active, they are known even more, and their reputation often precedes them. Bards sing of their deeds, nobles gossip about them, powerful people try to have them marry their daughters, sons, or other relatives. People come to them for help, not just of the "go and kill what threatens us", but also and even more of the "can you put in a good word with the king about my petition for a iron ore monolpoly?" variety.
Fortune is a result of fame and the challenges overcome. The PCs do not have to worry about money anymore. They have earned riches, and even without gold their name alone will pay their way in many places, and a lot of people give them gifts in the hope of earning a favor. The PCs have estates, or otherwise granted and secured income, and do not have to count coins anymore. Ressource management is not centered around cost, but about access - how much have the PCs on them when they need it? How long would it take them to get back to their vault to get the thingamablob they need?
Power is the result of fame and fortune. Not just personal "I can kill you" power, but also and even more influence. In most places, the PCs won't get hassled by the guard - or even the nobles. Even powerful enemies often have to tread very carefully when opposing them, to cover their tracks. In some places, the PCs are above the law even - and in a few more, the authorities will take their word over that of most others. PCs are feared by some, and fawned upon by others, and can save or ruin someone with a few words. People come to them seeking employment, favors or help, trying to profit from their power, and PCs rise high in their repsective circles.
Generally, challenges are easy to scale, with the CR system, but often fail to give that high level feeling since the relative power remains the same. You may cast an improved fireball, but the enemies can soak the damage at 14th level as the enemies soaked the damage from a regular fireball at 6th level.
So, to really get a high level feeling, one needs to show the power of the PCs relative to the world. That's where fame, fortune and power/influence come in.