Is there a systematic way to do this?

I don't seem to know the trick. I tighten the central bolt too much and the brake binds up, I loosen it too much and all the spring force goes to one arm (the one away from the cable anchor), there seems to be a magic middle point but the only way I find it is through trial and error.

I like to run my brake calipers very closely adjusted (pads 1/8" from rim) so centering is important.

This question is referring to the older single-pivot type. I have Mavic 410, Weimann 605, etc and have the same frustrating experience with each. I don't have any bike with dual-pivot sidepulls.

The central nut in front should not be used for centering. That is to hold the brakes together. Mount the brake. I sometimes squeeze the brakes against the rim with my hand, while tightening with the other hand. You can also try tightening the mounting bolt with the brakes a bit off to one side and sometimes it will move to center as you tighten.

One more technique is to center & tighten as best you can. Then place a small punch or flat blade screwdriver on the spring, and tap with a hammer to move the calipers until they are centered. I used to have a punch that i had ground the tip with a curve to match the spring shape. Helped it stay in place better.

Also make certain that your brake cable housing is neither too long nor short such that it exerts force on the caliper pushing it sideways. There are also usually wrench flats or notches between your brake arms and the frame. A thin ignition wrench or a tool like this: https://www.amazon.com/Park-Tool-OBW-.../dp/B001B6LPA6 can be used to rotate the caliper into the correct position.

It would help to know what bike or what model caliper you are working on - a pic would be ideal. Faling that, if there is not a set of flats at the back of the caliper (common with bikes from 80's and before there is another technique for centering. First make sure the pivot is adjusted so that the arms move freely side to side but not forward and back. Then lock the two nuts together firmly. To center, put one wrench on the nut that holds the caliper on the frame and the other on either the forward or back pivot nut - the forward one if moving the caliper clockwise, the other if moving counter clockwise. Move the two wrenches in tandem until the brake is centered. This method usually allows finer adjustment than the hammer and punch method.

Latest brakes I've installed, on Monday, are Mavic 410.

https://velobase.com/ViewComponent.as...74957&Enum=117

There is only a nut (in my case, a recessed nut) on the threaded mounting stud, and a domed Allen bolt on the front of the brake.

I guess that calls for the process just described by cny-bikeman?

Yes, usually the same technique can be used on that type of brake. Make sure the mounting bolt is not extremely tight when you do the procedure - once centered you can tighten it further without affecting centering. Also make sure the cable housing has a gentle bend, as either too little or too much housing length from the last stop or housing guide can push the caliper to one side.

Park Tools sells a couple of thin wrenches (OBW-3 and OBW-4) intended to center single pull calipers either by holding the nuts or flats behind the arms or by straddling the brake spring while the mounting bolt is tightened. Look here: https://www.parktool.com/category/brake-tools

It's nice when you can get a wrench on it to adjust, but a flat blade screwdriver and hammer work also, tap the spring

Yes, covered above already. The OP noted that he is going to need very accurate adjustment, which is why we are offering other alternatives. As it happens a Google image search for those calipers indicates that indeed they do have centering flats, which I believe are 10 mm.