After a major earthquake, are any of the insurance companies going to be around to pay our claim?

While this is a very common concern, it actually has no basis in reality.  According to the Insurance Information Institute, the Northridge Earthquake (January 17, 1994) was the costliest earthquake in U.S.  history in terms of insured losses (both actual and adjusted for inflation) with a total of $20 Billion (2013 USD) in insured losses.  While 20th Century Insurance came close to collapsing under the weight of their earthquake claims, there were NO carrier insolvencies resulting from that event.  Every carrier (including 20th Century) made good on their obligations to their policyholders.  Fast-forward 20 years, and present-day carriers have extraordinarily sophisticated computer programs at their disposal which help them manage their accumulations along known fault lines.  This, combined with greater reliance on risk transfer (through both reinsurance and emerging capital market alternatives), increasingly vigilant regulation both by the state and by independent rating agencies, and the unprecedented amount of surplus funds available in the current marketplace, significantly reduces the probability that any well-rated carrier will find themselves over-exposed after the next earthquake.