Finding successor chips
I have a few general obsolescence strategies.


Check the original manufacturer's website and look up the PCN (product change notice). Most big manufacturers will publish these any time there's a meaningful change to a part (new rev, new fab, end-of-life, last-time-buy, withdrawn, etc. They sometimes recommend fit-form-function replacements or migration paths to new devices.
Check other manufacturers and see if there's a cross-reference for the obsolete part (or one of it's manufacturer-suggested alternates).
Do parametric searches for parts in the same family (i.e. opamp) specify the specific (no pun intended) parameters that most concern you (packaging, pinout, power, capacitance, etc.) and see what you get.