Before you sign a contract, work with your administrators to define what kind of support is essential. Quality support providers will determine what action is appropriate based on the support level you choose. To help define what you need, compare support models and vendors.
Ask service providers to show you any data that backs up their claims. This won't necessarily provide you with undeniable proof of a service provider's excellence, but it says something for the provider's business acumen.
Support from your hardware and software vendors, and their relationships with Linux OS vendors, must be considered as well. Your hardware provider or independent software vendor should agree to remedy Linux OS defects involving particular hardware drivers by incorporating necessary patches in all future releases of the distro.