How do you get a customer to go on the record with a testimonial quote or case study?
Cultivating a relationship with a B2B customer that is deep enough to work with you on a case study is a long-game play. It's a big ask.
Put yourself in your customer's shoes. You are asking them to work with a writer through multiple drafts and reviews. They may have to submit the piece for internal review by their brand team, and potentially PR or legal.
Some customers have a blanket policy against associating their brand with a vendor in any way. Of course, this is something you want to get out of the way early, before investing time on either side.
Marty Cagan talks about building a pool of about 6 reference customers. This requires making a personal investment in a select group of customers to develop a deep level of trust and reciprocity.
When considering a prospective reference customer, look for customers with something to gain from being associated with your brand or product, or who have a vested interest in helping you succeed. Your sales and CS teams probably have insight into potential relationships that could be developed into reference customers.
In the short term, any time you are doing customer discovery, keep your ears open for quotes that demonstrate your product adds value. When the interview is over, ask them if they would be willing to allow you to use their quote in your marketing. See if your Sales and CS leaders can help collect leads for quotes, too.