I have posted loads, never had one damaged or delayed.
Use a box where the saddle fits quite tightly. Use bubble wrap over the hard parts, such as pommel and cantle. Make sure it won't slide around in the box, the better size the box is, the less packing you need.
I have shipped using Hermes even and it was all OK. I always do signed for. You can choose to have extra insurance if you want.
NOT HERMES!
I have had saddles wrecked arriving and wrecked after departing from them.
I now wrap in about a thousand layers of bubble wrap and a big cardboard box packed out with paper or more bubble wrap. I tend to use parcel force 48hr ?
My DH always uses Parcelforce - usually next day AM delivery. Parcel is tracked from start to finish. As others have said, use a good sturdy box relevant to the size of your saddle - the last thing you want is it sloshing around inside all over the place. My DH uses offcuts of foam and latex to pack his saddles so they are snug in the box, but bubble wrap, polystyrene or paper is just as good. Secure the box with parcel tape top and bottom.
Always take photographs of the saddle before packing, and the box after it is packed and ready to be posted, just in case it is damaged in transit.
Also, please bear in mind delivery companies are really stretched at the moment - so it may take a little longer to be delivered than usual.