The most important thing to an organisation outsourcing all or part of their IT Support is to make sure that the organisation handling it on their behalf are capable and have experience in dealing with the software and systems they use.
This is not because they need to do your work, but they need to understand how your software operates and how it resides on your network. This will allow them to provide you with the most stable platform for your software to perform and your staff to operate on.
You wouldn't give someone a job without the relevant experience or checking out their references would you...?