This depends on the nature of the squeal. Some combination of the brake arms, fork legs, brake cable, pads, headset, etc. are resonating at a specific frequency. You either need to increase the damping with stiffer components or shift one or more of the offending natural frequencies to where it not longer causes a problem. I got rid of the squeal on my Soma Double Cross by doing several things:

I tightened down the headset to the point where there was absolutely, positively no play at all. It is probably a little too tight but if I wear it out I can install a Chris King. This eliminates some feedback from the fork flex/movement pulling on the brake cable. Less feedback = more damping.

I replaced the link wire with the next longer version. I think I went from a Shimano "F" to a no-name "B" that was in the LBS's junk box. This reduced the leverage that can be applied to the brakes with through the levers and the fork flex/movement. Less leverage also means less feedback.

These two tricks got rid of about 30% of the squeal for a grand total of $1.

I then found the right set of brake shoes. Salmon Kool Stops did the trick for me. Their black ones were actually a step back from the Shimano pads. The severe conditions pads are a bit harder and tend to raise the resonant frequency of the brake arms/pads. I also toed them in about a "penny's worth" more than the Kool Stop instructions recommend.

I used to have a love/hate relationship with the Canti's on my cross bike. Now I love them when I'm out riding with the roadies. I can brake so much later and aggressively that it's a lot of fun when we're riding through twisty stuff with bits of gravel and potholes.

There are numerous other fixes as well: cleaning the rims with fine steel wool or scotch-brite, moving non-threaded shoes further in or out, putting spacers behind threaded shoes, wider rims, stiffer forks, stiffer brake arms, compressionless cable housing, etc. Keep experimenting and paying attention to the frequency as well as the volume. Lower frequencies require more driving force to oscillate. Higher ones are more easily damped.

One more thing. Good luck. This problem often requires A LOT of patience.