The world’s highest tennis court is in the luxury hotel Burj Al Arab in the United Arab Emirates (Dubai). It is the 4th tallest hotel in the world. The hotel stands on an artificial Island about 280 m or 920 ft. out from Jumeirah Beach. The hotel itself looks like the sail of a ship. If you look closely at the photo, you will notice a round bit jutting out on the right hand side, that is the tennis court.
If you would like to learn a bit about the construction of this hotel, there is a bit of information in Wikipedia.
The video below is of Roger Federer and Andre Agassi playing tennis on the court at the Burj Al Arab. It is actually a helipad area that gets converted to a tennis court. It’s a shame it isn’t a real clear day, but still the scenery is spectacular.