Testimonials are perishable
The single most useful thing to understand about testimonial collection is that willingness is a moment rather than a state. A customer who has just told you that something worked well is, at that instant, more willing to say so publicly than they will be at any point in the following month. Most collection processes ignore this entirely, running quarterly requests that arrive when the feeling has passed.
The fix is organisational rather than clever. Anyone who speaks to customers should be able to say, on the spot, would you be happy for me to use that, and then record the answer somewhere findable. That single change usually produces more material than a dedicated campaign.