We always start and end with personal recommendations, but you're right that doing so can be difficult to get for specialities.
Read their biography on the hospital web site. How does it compare to their peers on the same staff? Does your pediatrician know the other doc, or just their reputation? Can your pediatrician comment on the facility as a whole?
Who are they affiliated with: a university, and/or a big hospital, or just private practice?
Hit the web and search out their names. Do you find recent publications (indicating current skills), or participation in conferences/education, or any articles discussing charity work?
Last, ask your pediatrician for multiple names, and have an initial meeting with more than one of them. It's your child's health, so feel free to shop around as long as you have time: we got the name of a dermatologist, but they weren't taking new patients so we got someone else in the same practice. Well, we didn't like them, but then we found a third doctor who we got along with well and who gave us sound advice with clear explanations. It's hard and can take extra time, but it's worth it to meet a few people before choosing.