The reasons behind cathedral ceilings are aesthetic, not performance-derived. And you should take it into consideration.
Cathedral ceilings have obvious disadvantages. They are a cause of higher energy consumption, in most climates. And they can also be source of problems: condensation, rot, ice dams, air leaks.
Though it is possible to build a cathedral ceiling without the problems listed above, it's not easy, and it is a lot more expensive than a common pitch roof with a flat attic. If you are going to build a new home, think twice before choosing a cathedral ceiling design (or a flat roof).
These page deals with insulation improvements of existing flat and cathedral ceiling roofs.
Roof cavity insulation
To improve the insulation of cathedral and flat ceilings you need to fill the whole cavity, or to fill it as much as possible. New Homes & Cathedral and flat roofs & Energy improvements
If you are going to build a new home, think twice before choosing a flat or a cathedral ceiling roof. Flat roofs are prone to water leaks and damages, while cathedral-vaulted ceilings are difficult to insulate and prone to moisture problems.
Besides, higher ceilings – though they may be charming – make rooms more difficult to heat and cool. They aren't an energy efficient option for cold and mixed climates. A pitch roof with a flat attic is a better option for energy savings.
Obviously, that is rarely enough; the cavity may be only one foot deep, or less...
Choosing an insulation material with a very high R-value per inch (sprayed foams) may help a little, but not much.
To improve significantly the insulation of cathedral ceilings or flat roofs you may have to do more than just adding insulation to their close cavity.
Cavity Ventilation issues
The insulation of closed roof cavities also raises the question of whether to leave an air-space for ventilation.
Experts often disagree about it, though there is an increasing consensus about the advantage of filling the entire cavity - as long as the risk of moisture intrusion is minimal. Ventilation is only clearly advantageous in cold-humid climates. Moisture has to be kept out of the cavity.
Ideal levels of insulation in cathedral ceilings and flat roofs
Ideally, the levels of insulation in flat roofs and vaulted ceilings should be similar to those used in open attics: R-40 to R-60. See: Recommended Levels of Insulation. That's critical to prevent conditioned inside air to migrate through the materials in cold weather, and to prevent outside warm to move into the living space, in hot weather.
How to add extra insulation to existing Cathedral ceilings
Whenever feasible, consider the following (it's expensive, but there is no other way to overcome the constraints put by the limited depth of the roof cavity):
1 - Add a high layer of foam insulation (sprayed foam, or rigid foam) below the existing roof, on the top surface of the ceiling. You will not have to fill or add insulation to the close cavity of the roof, but you will need to re-roof...
2 - Add a layer of foam insulation (sprayed foam, or rigid foam) from the interior up against the interior finish of the ceiling. Obviously, you will have to install a new interior ceiling finish.
How to add extra-insulation to flat roofs
If you own a flat roof (or a near flat roof), consider adding a new pitched roof over the existing structure. You will get a open attic that you can insulate to high levels.
When feasible, that's the best way to dramattically reduce heat flow through the ceiling and to minimize the risk of water leaks.
Vaulted and cathedral ceiling insulation improvements are tricky and require proper equipment and know-how. It's not a DIY job.