No access to CNC or plasma cutters
Even though etching would be your best bet, trying to align both sides would be a pain (If you etched it yourself). So, if you are patient and have one, a Dremel or the like with a flex shaft and some cutting bits might work.
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Aligning the two sides is VERY easy. Steve
A jeweler's saw is made for this kind of work, but complex designs will take a while to cut out. Etching is definitely your best bet. If chemical etching doesn't appeal to you, consider electro-etching. It's cleaner and less toxic than most types of chemical etching, and gives a straight-sided etch (no undercutting). Given the straight sides, you could probably etch all the way through your brass from the front and no have to worry about matching your masking front-to-back. Check here for detailed information about this technique, including how to make the necessary equipment out of a battery charger and a few easily obtainable components.
Extending my very brief comment, see if you can find a local PCB fabrication shop. Now there are two ways to go, ask nicely and the guys I know will coat whatever I want with their special sensitive films for a few bucks. Supply them with pristine, clean, polished metal sheets, and they'll let you have photosensitised metal back. Print your patterns on to transparency film with a good laser printer, and then expose a sandwich to UV light, then etch with either ferric chloride (yucky, not recommended) or cupric chloride (nice !) The alternative is to let the PCB shop do all the legwork - be warned though, you may still have to etch it, brass might contaminate their process chemistry for etching. Steve
People who build model trains often use intricate brass sheet, and like steve says, they're etched. Look up PCB etching for ideas. L
You might try gluing it to thing plywood then cutting it with jig saw or band saw. As long as the cutting stroke was on the down cut not the up cut. You could try etching it. There is an instructable for that. Something like that might work. I don't know how intricate your design is. If you want to try, you might do the pattern in straight up and in reverse and put it on both sides. That way the acid wont be attacking the rear face.