With any luck, you'll never see a police badge up close. And even if one is flashed in your face, afterwards as you're sitting on the curb wearing zip-ties you probably won't be thinking "Gee, I wonder how those badges are made."
But for those who are curious, a Brooklyn-based company called United Insignia has a video up showing the process. We always assumed the NYPD's "shields" just came out of a stamping machine, but there's actually a fair bit of handwork involved:
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According to the NYPD quoted here, the current design dates back to 1902. Here's their description of the production process:
Our modern shield is made of nickel silver. It is first die-struck in a drop hammer which gives it impression and then is pounded until the desired height of the characters is reached. The perimeter is then blanked and embossed and the numbers and lugs are hard soldered. The badge is then dipped, cleaned, nickel-plated and polished to a high gloss.