Normally, you bill your customers on an hourly basis. If you do your support remotely, you have a great opportunity to make precise calculations based on your connection history statistics. Here, web-based solutions are a good choice, as they often allow seeing your sessions history for any given period, with details like remote machines’ IP addresses.
You might as well want to export the session stats and use them to invoice your customers via SalesForce or a similar solution.
Most often, you would charge for remote support less than for on-site visits. Still, while traveling to a site, you might have an opportunity to work on-the-go for some other client :)
Examples of tools that provide connection statistics: TeamViewer (paid version only), DeskRoll, SkyFex.