In most cases* to receive reimbursement for out-of-network services by a provider requires that you have a PPO insurance plan. Every plan has different levels of deductible and reimbursement rates and the amount of the money you get back will depend upon your individual plan.
To learn exactly what your benefits are, you can check the online portal of your insurance company or call them directly. Alternatively, if you get your insurance through your work, you can reach out to your HR representative who may be able to provide benefit info.
* Out-of-network services are sometimes covered by Preferred Provider Organizations (PPOs), Exclusive Provider Organizations (EPOs), Point-of-Service (POS) plans and High-Deductible Health Plans (HDHPs) which may be linked to health savings accounts (HSAs may have out-of-network benefits). Also, some HMO plans can pre-authorize a service for out-of-network, if there are no local in-network practitioners who provide specialized care.