The saddle should sit behind the shoulder, not on it, so it does not restrict the shoulder movement. Run your hand over the shoulder and you should feel the scapula cartilage - the saddle should sit behind this.
On very forward cut saddles look for the point pocket, see Parts of saddle, and make sure this is behind the shoulder.
The saddle should only sit over the thoracic spine i.e. the spine to which the ribs are attached. Beyond this point is the lumbar spine which is weak and not weight bearing.
To work out where this is you can feel for the last rib and follow it up - remember it will curve round to join the spine. Or an alternative and easier way of finding it is to find the whorls on the haunch (follow the line where the hair runs upwards) and measure a hand span plus an inch.
This is one of the most important points to get right when saddle fitting and you should always consult your saddle fitter .
A saddle which is too narrow will pinch the muscles (see The horse section) so they cannot work efficiently and will inhibit the movement of the horse. It may sit up at the front which will pitch the rider's weight to the back of the saddle causing pressure points. A saddle which is too wide will pitch the rider forward and may even put direct pressure on the bony spinous processes
The most accurate way to measure the width is to take a wither pattern. this can then be placed in the front of the saddle and it should fit closely.
Taking a correct wither pattern requires training and practice so it's best to ask your saddle fitter to do this.
There are other giveaway signs that the saddle is not the correct width.
You should be able to fit 3 fingers under the pommel.
Also the saddle should fit the shape of the horse so there is even pressure down the front of it.
In this example the saddle is too narrow. You can see the points are digging into the horse and there is more than 3 fingers clearance
In this example the saddle is too wide. The points are not even touching the horse so all the pressure will be at the top and possibly on the withers as here is barely any clearance.
The saddle should sit on the horse with even pressure down the front and along the back when girthed.
Run your hand palm up down the front of the saddle.
Then place your hand palm down right under the saddle by the stirrup bar and run your hand along the length of the saddle.
It should move freely and not be blocked at all.
The fulcrum effect of a curved tree is shown here - all the pressure is felt through the middle and my hand got stuck at this point
Please note this is not a comprehensive list of every single check, it's designed to inform you about the general principles. Always consult your saddle fitter on a regular basis.