How do I know if I can trust a particular locksmith?

Do your research – A good, genuine, professional locksmith will be more than happy to provide you with references or guide you to their online customer reviews such as Facebook or google reviews.
Some Locksmiths will voluntarily pay to be a member of a trade website such as Trust a Trader, however this is not compulsory and comes at a substantial cost to a locksmith. So if a locksmith chooses not to be a member of such a trade website, then this is most likely because of the financial implications rather than a reflection of his or her professionalism and competence.
Also, call the locksmith and speak to them, they will be more than happy to offer free help and advice and it’s a good opportunity for you to judge for yourself after having a chat with them.