Here's my tip: offer value! Have a conversation, spend the first couple emails consulting them for free. For example, talk about their site loading speeds and how it's hurting customer experience as well as Google rankings. Send them screenshots from Pingdom, and show them strategies on how to improve their site speed. This doesn't take too much time and what you're doing is creating a genuine human connection with the prospect.
After you warm the client up, hit them with your offer. Don't be afraid to sell to them! You've already offered so much free content.