You're looking for an Errors and Omissions insurance policy, likely from an insurer who has a special product line for tech businesses. Word to the wise: many of these insurers, despite having that product line, are effing clueless about technical reality. The best reason to have an agent representing you is that you won't have to educate an underwriter on the difference between on-premises and off-premises SaaS. (I have someone I can recommend -- email me if you want her contact information. Her assistance was very sanity-saving during the process.)
Your E&O policy may be bundled with a General Liability policy. GL protects you if someone slips and falls at your office, E&O if your software breaks and causes damage to customers' businesses. The fact that GL involves vastly more work, exclusions, and cost should tell you something very instructive about the insurance industry's estimation of the likelihood of having to actually pay out on your E&O insurance. [+]
You're going to use the fact of this insurance policy to drum up additional business for yourself. Given that, it makes sense to pick a nice round number. I'd suggest $1 million, which you'll find is the practical minimum anyhow.
Kalzumeus Software and Appointment Reminder share an E&O/GL policy, with an extra (priced) endorsement for data breaches and regulatory defense (i.e. HIPAA). The policy was priced based on a combination of how we earned revenue (consulting vs product income vs training, etc), how large we were in employee count, what industries we worked in, and our gross revenues.
Our policy costs on the order of $2,000 a year. Speaking with business buddies of mine, you'll find that that is roughly ballpark for most firms with less than 10 or so employees engaged in, roughly, "our line of work."
You'll find that who actually insures you is treated as a boring implementation detail, particularly if you buy through an agent, since they'll come up with a few quotes and you get to pick on a price vs. features comparison. The name on our policy is Warren Buffet's professional liability company, US Liability Insurance.
[+] So I checked my policy. Although this was not how it was explained to me, the policy describes roughly 15% of premiums going to GL and 85% going to E&O. Assuming that is accurate, that means they -- sensibly -- think I'm more likely to be sued for nuking a server than for dropping a Macbook on someone's foot.