Handwriting is still useful in some contexts (for instance, my husband is applying for a new job and it must be done on paper but we don't have a typewriter, so his handwriting skill suddenly becomes relevant) but I will be surprised if it is anything but an art form by the time our kids are grown. Considering that future, I see it not as a necessary tool but just one of those things that some people might choose to be interested in pursuing; like I choose to play piano. In that future someone who doesn't isn't disabled; it's purely a personal preference.
Its future relevance is arguable though, and I respect your concern.
So. Like with reading, they will want to do it when it becomes useful or interesting to them, but of course a reading-rich environment is both a resource and makes the transition easy because it's just part of life. There have been lots of good suggestions already... I have a few to add. First, do it yourself. In our family, I can hardly do anything by myself (that I want to do) without the kids wanting to do it too -- so
much so that it gets annoying sometimes.
Get some calligraphy pens and ink, and explore it as an art form. Make art, and make writing part of your art. Start writing in a journal by hand. Etc. Drawing also in itself increases fine motor coordination and confidence with the pen.
We have friends who keep a lined notebook in their bathroom -- in the morning and at night while they're getting ready for bed or to go off for the day, family members write little notes to each other. Sometimes reminders, or pertinent information, but sometimes just things like "It made me smile to hear you singing today" or "I love you." It's both a nice and a useful thing.
Another idea is a chalkboard -- we painted a wall in our kitchen with chalkboard paint (and actually any dark paint will do) and that's where I write my grocery list and things I need to remember. The kids have their own ideas about what they want to eat and what I need to remember
so they often write there too.