For an example of the results possible when converting to B&W after shooting, check out The Ian Curtis biopic
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This was shot on colour film, and digitally graded to B&W. The resulting film looks fantastic. (Apparently the director wasn't happy with the excessively grainy results he was getting by shooting on B&W film.)
The real test would be a film shot on a digital format in the first place and converted to B&W, but it gives you an idea of what's possible when creating B&W by digital means.
One very important consideration is that you need to choose and shoot your subject with B&W in mind. To use Blapto's example, a stunning picture of a rose in a garden wouldn't look as good in B&W, however you processed it, as it relies in colour for impact. Go for something with texture and contrast, where colour isn't important, and you'll be on to a winner. B&W requires a different mindset and sensibilities to colour.
On the technical side, for anyone who's interested in recreating a classic contrasty B&W film look in Photoshop, try using Red Paw Media's
bleach bypass filter, and then converting to greyscale.
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