Also, if you're looking to niche and don't have a client in the chosen industry, you can use other success stories in the industry to the same effect.
Our first client in one industry we got because I set up a meeting with one of the companies in the industry that had recently made a large update to their website like we would like to do for others in the industry. Sat with the COO that told me all the improvements they've seen, increased revenue, & other advantages to the website overhaul. I took that info to another similar (but not direct competitor) company and said we could offer the same advantages with a similar product. Literally walked into their office and introduced myself, gave a business card, then followed up with a few emails to various people in the business until the Owner called me up one day out of the blue. Had a contract signed a month later.