If they are custom, finding the same cabinet company to build the lowers and a simple revarnish of the top cabinets could have you looking good as new.
If they are prefabbed cabinets, you may be able to find the manufacturers information on the backs of your drawers or other odd places within the cabinets. If you cannot find them, going to a big box store who carries many different brands with samples would be a good way to find the best match. Get multiple estimates because cabinets can be one of those things that a similar item can vary in cost by thousands of dollars dependent on who you are paying to install. Also take this time to think about your layout, add the drawers that you have been wishing for!!!
What if you cannot find a good match? You have a few options here, getting unfinished cabinets in a similar style and painting both to match is a good bet. I ran into this situation in my own home and decided to get creative! We painted our bar with an accent color, then did the upper cabinets painted and lower cabinets stained. It turned out beautiful. I would also suggest to use apps like Pinterest to find the right combination for you.