Most testimonial requests I've seen go out as an email, a few days or a week after someone signs up or buys. By then they're busy with other things, and a lot of those emails never get a reply.

So in testimonialsltd we added a second way to ask. You put a small prompt inside your own app or site, and you decide when it shows up. Like right after someone finishes onboarding, hits a milestone, or renews. It asks "How's it going so far?" with a star rating. If they pick 4 or 5 stars they go to your testimonial form. Below that, they get a private box asking what went wrong, and that only goes to you.