Use Net Promoter Score to get more reviews in two-steps.

First question: How likely is it that you would recommend my brand/product/service to a friend or colleague?

When the customer rates this question, the second question appears:

What’s the most important reason for giving us that score?
If your customer gives you a score of 9 or 10, they get an automated email that politely asks them if you can use their comments in a review. Tools:
https://usercompass.com/
https://delighted.com/