What is the best saddle pad with shims?

Do you mean pads with built-in shims? Because you can buy shims by themselves to use with any pad. 

built in pockets for shims so you can vary the thickness.

Len Brown's Corrector Pad.

www.thecorrector.net

It's a crazy website to navigate though.

Diamond makes a shim pad.  I have one and like it. 

https://www.diamondwoolpads.com/collections/pressure-relief 

I agree with The Corrector/Protector by Len Brown. Agree his website is a hot mess but his pads work. 

I love Darla Schneider pads and she makes a shim for the withers or a full shim.  I have the full shim for one of mine who has a kind of odd high wither, balances it out very nicely. 

Ditto on this.

Has 3 levels of shims on all 4 corners. Love it!

I've had good luck with ThinLine.

I got frustrated with traditional shims and bought a 5 star shim with velcro. Goes on any pad and when you place it, it STAYS!  I was about to spend another $300 on a thicker pad when I found this jewel for 30 bucks. 

thanks I am going to check into that.

I got a CSI pad and put their shims in it.