Get it in writing
A clear written quotation is the first sign of a contractor who works properly. It should set out what is included, the materials, the access arrangements and the price, so there are no surprises later. Be wary of a figure given off the cuff without anyone looking at the roof.
Ask about access and safety
Working at height safely needs the right access, which usually means scaffolding for anything more than a minor repair. A contractor who plans access properly is one who takes the work, and the people doing it, seriously. Ask how they will reach and work on your roof.
Expect an honest answer
A good roofer will tell you when a repair will do and when it will not, rather than selling you a new roof you do not need, or patching one that is past saving. Honesty about what the roof actually needs is worth more than the lowest price.
Local and contactable
A contractor based in your area is easier to reach, quicker to come back if anything needs attention, and has a reputation locally to protect. Being able to talk to the person who will do the work, and reach them afterwards, counts for a lot.