Naturally, you would like to ask for a list of testimonials on their service credential. Look closely if such testimonials are fabricated because it is rather easy to say that "The following list of companies are our customers and are happy with our service". If the testimonials bear proper company and user names, it is likely to be authentic. Do not be taken in by references such as big "ABC" company because any one could quote such references without obligation.
One should also ask around friends, relatives, technical vendors and colleagues. Through words of mouth, you will be able to make a better judgement.
If you are not able to get good info, seeing is believing. Why not pay the selected a visit? At least take a look at the web sites or simply call in for an enquiry. Do they appear helpful and professional?
Another helpful hint is that a truly trusted data recovery company would have built up partnerships with many other trusted companies, be it educational institutions or computer stores. Look for such capabilities and track records.
If the data recovery facility you choose does not have adequate facilities, proper equipment, staff, skills and experience, you will lose your chances of recovering data due to their incompetence.