> Some fonts as for example Lucida have a calligraphic style called up with \cg.
> If it is not present a default is taken.
> However, I would like to take other action in that case, for example switching to another font.
> 
> Thus, how to test on the presence of that calligraphic style in the current font?

It depends on the font, whether it has a calligraphic variant.
In the case of Lucida, its name is "Lucida Calligraphy".
There's also a "Lucida Handwriting".

You can use it in ConTeXt because there are some default typescripts 
mapping that font on the \cg fontstyle.
You can look at these files in your ConTeXt distribution:
/tex/texmf-context/tex/context/base/type-imp-lucida-opentype.mkiv
/tex/texmf-context/tex/context/base/type-imp-lucida-typeone.mkiv

If you want to use a different font, for which there's no default typescript, 
you have to write your own typescripts.
You can also mix font families, taking the missing calligraphic variant 
from a different family with a similar look.

Hope it helps,
greetings,
Massi