Shearing back the nepeta after the first bloom flush - like one would do with hardy geraniums - generally produces a new round of flowers. Deadheading crocosmia will not encourage any more flowers. Most bulbs and corms don't work that way :-)) But the seedheads are quite attractive and make a great dried flower accompaniment.

I disagree; by preventing the Crocosmia from making seeds more nutrients will be stored in the corms for the next growing season. It may result in more flowers next season.

That's possible, but deadheading Crocosmia won't produce more flowers in the current year, which is what I believe the OP is asking about. Anyway Crocosmia doesn't need any encouragement so I wouldn't bother deadheading. Quite apart from it's being fiddly and time consuming. For the catmint shearing the whole plant is fast and effective. It doesn't need deadheading as such.

Thank you @gardengal48 (PNW Z8/9), @iochroma and @floral_uk z.8/9 SW UK! I am going to shear the catmints today.