First, when pitching businesses, let the prospective client know up front that you don't live where they live. You want to begin building trust right at the beginning.
Second, provide references before the client even asks.
Third, show them work often. This is the best way to chip away at a client's natural situational anxiety.
Fourth, be very available. Since you can't meet face to face, you better return phone calls, emails, instant messages, etc. This is basic business stuff, but it's tenfold more important when youo're working remotely.
Lastly, get the client involved and let them follow along. Make sure they feel that this is their project too.
The old adage still applies: No assholes allowed. But for remote work, you need to extend it to no asshole-y behavior allowed, no drama allowed, no bad vibes allowed