How do you write a follow-up email without saying "just following up"?

Write each follow-up as if the first email was never sent. "Just following up" adds zero new value — it is a guilt trip, and the prospect did not lose your email, they chose not to reply.

Instead, lead with something new: a fresh data point, a peer comparison, a different angle on the same problem, or a free attachment they can use without replying. Done well, a value-led second touch out-replies the first by a wide margin.