Something specific to servo presses that gets overlooked during die changes — don't just adjust the mechanical shut height. Most servo presses have an electronic BDC offset parameter (on Komatsu it's in the recipe, on Aida it's the "slide adjust" screen). The mechanical adjustment gets you in the ballpark, but the electronic offset is where you do your fine tuning — 0.01mm resolution vs the 0.05mm you can realistically get with the mechanical adjuster.
The procedure I use: mechanical adjust to within 0.1mm of target, lock it down, then use the electronic offset for the last bit. This way the mechanical system isn't fighting the servo on every stroke. I've seen setups where someone cranked the mechanical adjuster way off and then compensated with a huge electronic offset — the motor was working 15% harder than it needed to on every cycle. Energy waste and extra heat.
The other thing — save your recipe BEFORE you start adjusting for the new die. I know it sounds obvious but I've watched guys overwrite a good recipe because they forgot to save-as first. On our Komatsu the recipe stores BDC position, speed profile, tonnage limits, everything. We label them by die number and date. When that die comes back in 3 months, you load the recipe and you're running parts in 10 minutes instead of 45.