A number of companies do testing to, say, 60601-1 for electrical medical device safety (i.e., Intertek, Nemko, UL, etc.). (Do note that I'm not endorsing or have any ties with the companies mentioned.) You generally want these to be accredited test labs. I presume that's not what you're asking about, though. There are plenty of mom-and-pop test shops to do basic functional testing (white / black box) which generally don't need to be accredited. A web search turns up a good many. Maybe note your specific needs?