$340 per month is about $4080 per year, which really does seem like a lot. Here are some tips:
Sell one car and share one car, easy way to cut this significantly. Pay the other car off entirely, and get rid of collision and comprehensive. Slightly less easy way to cut this significantly, but with the added benefit of no more car payment. Ideally, sell both cars, buy a couple of bikes, and get this drag off your plate entirely. :)
Raise your collision and comprehensive deductible. A deductible is the amount you would need to pay out of pocket before your insurance kicks in to pay for damage to your car. If you could easily come up with $2000 to pay out of pocket, raise your deductible to that. Different carriers will have different deductible limits.
GAP insurance covers the difference between your car's value, and what you owe on your financing, so your insurance can pay off the financing in the case your car gets totaled. Do you have GAP insurance, and where at? Some car financiers include GAP in the cost of the payment, and some require you to get GAP through your insurer. Check it out.
Check on how far your insurance company thinks you are driving one way to work/school. This can make a big difference in how "risky" you look to an insurance company.
Check on your credit score, and improve it if you can. Credit does factor into your "insurance score" (like a credit score, but for insurance), which is used to rate your riskiness as an insured.
Disclaimer: I work in insurance in Colorado, so this advice may not apply to California.. But! In Colorado, you can reject medical payments coverage, and also reject uninsured/underinsured motorist coverage. Medical payments is handy, as it can kick in to cover medical costs up to your health insurance deductible. UMUI is handy if you get in a hit and run situation, or if you get hit by someone without insurance, or without enough insurance to cover the damage to you/your car. I'm not sure if California will let you reject this or not, but rejecting it can lower your costs. That being said, if you *do* need that coverage, don't just throw it out. Insurance is supposed to be there for when shit hits the fan.
Check with your insurer, and see if you can qualify for any discounts when bundling with other types of insurance. Be careful with this! Don't buy renter's insurance or life insurance just because it will make your auto insurance go down - in the end, you'll probably just raise your insurance costs overall. Insurance is about offloading financial responsibility onto a 3rd party that weighs the risk of insuring you against the money they charge to insure you. Only buy the coverage you really need. Exploiting discounts is usually best done through an Agent who understands how to work their carrier's system.
All of that being said, there are some things that are futher outside of your control. For example, car insurance rates are more expensive if you live in a Denver zip code, as opposed to living in an Adams County zip code. They could be right across the street from one another, but still have a cost difference based on statistics. In addition, rates increased across all carriers in the Denver Metro Area this spring because of how many people are moving into Colorado. A broad situational shift like that affects the riskiness of driving in general, and so everyone gets a rate bump, even if they're a really responsible driver, or never use their car, or have been insured with Company Y for 30 years.
Hope this helps!
Kayla