You can do this with the code below, and the code in your question was actually very close to what you needed, all you have to do is call the cmap object you have.
import matplotlib
cmap = matplotlib.cm.get_cmap('Spectral')
rgba = cmap(0.5)
print(rgba) # (0.99807766255210428, 0.99923106502084169, 0.74602077638401709, 1.0)
For values outside of the range [0.0, 1.0] it will return the under and over colour (respectively). This, by default, is the minimum and maximum colour within the range (so 0.0 and 1.0). This default can be changed with cmap.set_under() and cmap.set_over().
For “special” numbers such as np.nan and np.inf the default is to use the 0.0 value, this can be changed using cmap.set_bad() similarly to under and over as above.
Finally it may be necessary for you to normalize your data such that it conforms to the range [0.0, 1.0]. This can be done using matplotlib.colors.Normalize simply as shown in the small example below where the arguments vmin and vmax describe what numbers should be mapped to 0.0 and 1.0 respectively.
import matplotlib
norm = matplotlib.colors.Normalize(vmin=10.0, vmax=20.0)
print(norm(15.0)) # 0.5
A logarithmic normaliser (matplotlib.colors.LogNorm) is also available for data ranges with a large range of values.
(Thanks to both Joe Kington and tcaswell for suggestions on how to improve the answer.)