Although there is a good possibility that the existing stone foundation can be "capped" or encased in new steel and concrete chances are that because you are in earthquake country the safest way to proceed would be to replace the stone with a new concrete and steel foundation. Contrary to popular belief 50% of the home does not need to be torn down in order to replace the foundation. And, if the job is performed by someone that does this kind of work routinely the level of disruption can be surprisingly mild.
While replacing the foundation is more costly then capping it, the costs to repair damage that your home could sustain due to an inadequate foundation could easily be ten fold. The best place for you to start is with an inspection of the existing stone foundation by a licensed structural engineer. He or she will examine the condition of the stone, mortar, surrounding soil, and any anchoring devices that may exist and provide recommendations with respect to its repair or replacement. These recommendations or "engineering", which are typically complete with drawings, can be used to solicit estimates from contractors that specialize in this type of work.
Your best bet in locating a contractor to perform this work is to get recommendations from others in your community who have had this type of work performed. You can also seek referrals from engineers, architects, trade associations like the National Association of the Remodeling Industry, or even from contractors that don't specialize in this kind of work, but who know of someone that does.
And remember, when all else fails your foundation won't!