Promptness: A contractor who keeps the appointment for an estimate is more likely to arrive promptly for the job and complete the project on time.
Communications: How a contractor responds to phone calls can be an indication of your ability to contact him after the work begins. If you must wait days for a return phone call, will the same occur after the job starts?
Insurance: Adequate insurance is important for your protection. Ask to see a Certificate of Insurance.
Written Proposal: A well written proposal will carefully describe what is included in the job. This allows both parties to clarify any omissions or misunderstandings. The proposal speaks volumes about the professionalism of the contractor.
References: Any contractor should be able to produce a list of good references. If possible, drive by a recently completed job and look at the quality of their work.