For reference, there are two main risks covered by liability insurance: "defense" and "indemnity." The former pays the costs of a legal defense, the latter pays a settlement / verdict. Most media liability insurance policies cover both, but can charge different premiums based on the "retention" for defense and/or indemnity, i.e. how much you have to spend before the insurance kicks in.
If the big worry is paying lawyers to defend a "frivolous" suit, then focus on the former; if the big worry is a "large verdict," then focus on the latter. A common way to save on the premium is to have a sizable retention -- like $20,000 or more -- but then have good coverage after that. If you get sued, you might have to eat the first $20k in legal fees, but won't get bankrupted by the legal fees or the verdict.