What should I look for when hiring a masonry contractor?

I’m planning some exterior work around a property and I’m trying to understand what I should check before hiring someone. For brick, stone, or block repairs, what separates a reliable Masonry Contractor from someone who just does basic patchwork?

I’d be interested in hearing what people normally check first—previous projects, references, insurance, estimates, material knowledge, or how they handle unexpected structural issues. Any advice from people who have hired one recently would be helpful.