Look for an arborist with professional credentials, such as certification from the International Society of Arboriculture (ISA) or a registered consulting arborist from the American Society of Consulting Arborist. Request references for work that the professional has done that is similar to the work you need completed. Ask for proof of insurance (personal, property, and workers compensation).
Find a Certified Arborist at: http://www.isa-arbor.com/faca/findArborist.aspx
Find a registered consulting arborist at: http://www.asca-consultants.org/find/index.cfm