Which car insurance companies will insure drivers who only have a learner's permit?

Yes, most insurers will cover a driver who holds only a learner's permit, usually through a policy held by a parent or guardian who serves as the licensed primary driver. Some carriers let the policy buyer designate a licensed primary driver, while others do not, so unlicensed drivers and permit holders may need to shop around. The premium may reflect the primary driver's record. Note that proof of insurance is required to register a car in most states, and driving without coverage is illegal in most states.