'their prestige' is a correct and usable phrase in written English.
Example sentence: The royal family has long enjoyed their prestige throughout the kingdom.
"Their prestige it at stake," explained the organiser, Basilio López.
It is this selectivity that gives these journals their prestige.
Restricting those honoured with a Nobel helps maintain their prestige.
The mullahs see a chance to regain their prestige and power.
Other growers use their prestige cuvées to highlight a single grape variety, usually grenache.
Rulers of great powers in decline often seek short, sharp wars to restore their prestige.
Their prestige and (sometimes) higher quality tend to lead to higher-paying jobs.
The awards are coveted for their glamour as well as their prestige.
"If just 30% had opted back in, it would have been a blow to their prestige.
You give Ahmadinejad or Raúl Castro or Chávez a forum for their prestige.
Their prestige has risen accordingly, while the navy has struggled to assert its relevance.
