You are not smart carrying minimum limits for the reason you just mentioned. Your insurance company is only responsible to pay up to the limit of liability coverage. After that.....the balance is yours to take care of and the other parties insurance company or attorney will come after you for the balance.

Minimum limits should be 100/300 for liability as well as carrying 100/300 for both uninsured and underinsured coverage.

If you have considerable assets to protect a million dollar umbrella policy is also necessary.