Take it to the post office. UPS charges an arm and a leg and does a shoddy job. My first shipping experience ran me $90 and arrived at the location badly damaged (even though marked fragile). The next one was shipped via USPS and was only about $20, including a box and packing material.
I pack the saddle well in the smallest and thickest box I can fit it in while leaving enough room for packing, then I fill in all the empty space with air filled bags, bubble wrap, or something else. I can get all this free from work.
Then I take it to the post office. I've never spent more then $30 shipping a saddle and usually they're in the $20 range.
Spend the extra money and go UPS or Fed Ex with insurance. I sold a saddle and shipped it COD and the check was lost in the mail by USPS. It was never found and after months I was able to get a copy of the check which after some difficulty the bank did cash.
I bought a Butet off eBay and it was shipped USPS. Arrived quickly for around $20, if I remember correctly. I don't think it came all that far. Definitely was from somewhere on the East Coast. It was just in a box stuffed with paper and styrofoam peanuts.
I pack myself and ship UPS insured. I prefer UPS over USPS as the tracking is better, and they have to sign for it (i do not waive the signature requirement ever on big ticket items). I want that signature as proof of delivery. If you pack yourself and do the paperwork online, then drop off at te local UPS storefront, UPS is quite reasonable...taking something to the UPS store, having them pack and ship really increases the cost.
$20 is probably Parcel Post. Make sure that somewhere physically attached to the saddle is a name and address so if the box gets wrecked the saddle will be able to be shipped somewhere and not languish in dead letter. Use a good box, not one of those soft cardboards that Chinese goods are shipped in or some old display box that is preperforated so all your stuff falls out. Make sure the box is a good fit, not too loose. You can get Delivery Confirmation, Signature Confirmation, Insurance, some insurance with a signature, from USPS. Don't use ink that will run if it gets wet, if you preprint the label put clear tape over the entire front because that ink does run. If you preprint any label out of non-adhesive paper tape the whole thing down, don't leave any paper showing to get caught and ripped and tear the whole label off.
UPS makes their own labels with barcodes so they're a little bit better, but my saddle came UPS and they couldn't find the house, my MIL was kind enough to receive it for me and she got a little card in the mail and called them. My sender used a UPS store and they have separate tracking from regular UPS or did at the time - freaked me out that the number was bogus and I was going to be out XX hundreds of dollars - had to get the sender to clarify that this was a UPS store tracking number on the UPS store website, NOT UPS.com. Both UPS and USPS are beastly to parcels, there's stuff on Youtube that makes me wonder how anything gets anywhere without being smashed flat. Take pics and be absolutely certain that the tree isn't broken before you send it.
I do USPS now. I also recommend signing up for the online account where you can print your label off at home and then if you want to take it in you just drop it off or you can schedule to have it picked up. Online also saves you a few bucks. If you want a tracking # you have to go up to priority or the next one higher. I have found its cheaper than Fed Ex or UPS and I haven't had any problems with shipping it through them.
As someone else mentioned also you can get the same services, insurance, signature required Etc. through USPS. You can look up how much it will be to ship something through USPS as long as you have the zip codes and kind of know how big the box is and the weight. (generally 15-20lbs for an english saddle.) I can ship CA and surrounding states for 20-30$ but when we start hitting the east coast I'm generally in the 75-85 range without insurance, etc.
USPS is usually the least expensive route, however they have limitations on box sizes on International shipments, perhaps domestic as well. Check the website...
I have sent a number of saddles UPS and FedEx (preferred) and, as mentioned, one thing to consider is getting a double-walled box. Last time I shipped a saddle via International UPS they crushed the box. Although the saddle was fine (just a few deep scratches), UPS refused to pay a claim because the box was only single-walled. (Even though it was a very tough corrugated cardboard, it was crushed as there was only a single wall.)
FWIW--my uncle works for the post office fixing the large package sorting machine. He advised me that even if you make every best effort to mark the box as "fragile" or "handle with care", when boxes go into the machine they are basically dumped out of a truck and into the bin, large and small boxes together. If you can get some foam and wrap the saddle before filling the box with air pillows or peanuts, that may help avoid scuffing up the cantle or other more significant damage if the box is crushed.
Wrap it well (old towels or newspaper), wrap stirrups if including, stuff with newspaper or the air bladder things.
I've used both UPS and FedEx as both buyer and seller, and much prefer FedEx. If shipping to a home address, FedEx Home Delivery (you must request this specifically, rather than Ground) is very economical. I shipped an 18", well-wrapped County dressage saddle (heavy and large) last year for about $35 via FedEx Home Delivery, including insurance. I think the box was about $5 at Kinko's, and was very sturdy. (I bought the box there, but packed and shipped it myself.)
use whatever shipper you want but please please use bubble wrap and tape, and not the stupid Styrofoam peanuts they'll try to throw in the box for you at UPS... Those are a saddle receiver's worst nightmare, trust me! They will fly all over the place upon opening of the box, stick themselves under the panels and flaps... oh and they don't protect the saddle at all! They're just a mess!
The two times I did this I chickened out and took it to one of those postal places. They packed it and figured out the least expensive way to ship it. It was a privately-owned one, not one affiliated with one of the shippers or with Kinkos.