Using the Polar Stereographic Projection 'spstere'
, you can get the antarctic region by using e.g. boundinglat=-60
:
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
m = Basemap(projection='spstere',boundinglat=-60,lon_0=180,resolution='c')
m.drawcoastlines()
plt.show()

Note that 'spstere'
is always centered at the south pole.
In order to have a map, which is not centered at the south pole, you need to use the "stere"
projection. Setting the corners for the "stere"
projection is not straigt forward.
One may therefore use a plot in 'spstere'
projection and find some points which would enclose the region of interest. In this case e.g.
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
import numpy as np
m = Basemap(projection='spstere',boundinglat=-50,
lon_0=180+(-100+-30)/2.,resolution='c')
m.drawmeridians(np.arange(0,360,30),labels=[1,1,1,0])
m.drawparallels(np.arange(-90,90,5))
m.drawcoastlines()
xll, yll = m(-150,-70) # <-- find those points by looking at meridians and parallels
xur, yur = m(-30,-55)
m.scatter([xll,xur], [yll, yur], c="crimson")
plt.show()

Using those points, (-150,-70, -30,-55)
, as the corners of the map, you can then plot a map using 'stere'
projection.
m = Basemap(projection='stere',resolution='c',
lat_0=-90, lon_0=(-100+-30)/2., lat_ts=(-90.+-55.)/2.,
llcrnrlon=-150,urcrnrlon=-30,llcrnrlat=-70,urcrnrlat=-55)

If this heuristic method is not wanted, you may automate this procedure by creating a dummy map in 'spstere'
projection, calculate the coordinates from the rectangle in question (llcrnrlon=-100,urcrnrlon=-30,llcrnrlat=-90,urcrnrlat=-55.0
) and create a new basemap in stere
projection with them. The function below is taken from the ActiveState site (author PG).
from mpl_toolkits.basemap import Basemap
import matplotlib.pyplot as plt
import numpy as np
def polar_stere(lon_w, lon_e, lat_s, lat_n, **kwargs):
'''Returns a Basemap object (NPS/SPS) focused in a region.
lon_w, lon_e, lat_s, lat_n -- Graphic limits in geographical coordinates.
W and S directions are negative.
**kwargs -- Aditional arguments for Basemap object.
'''
lon_0 = lon_w + (lon_e - lon_w) / 2.
ref = lat_s if abs(lat_s) > abs(lat_n) else lat_n
lat_0 = np.copysign(90., ref)
proj = 'npstere' if lat_0 > 0 else 'spstere'
prj = Basemap(projection=proj, lon_0=lon_0, lat_0=lat_0,
boundinglat=0, resolution='c')
lons = [lon_w, lon_e, lon_w, lon_e, lon_0, lon_0]
lats = [lat_s, lat_s, lat_n, lat_n, lat_s, lat_n]
x, y = prj(lons, lats)
ll_lon, ll_lat = prj(min(x), min(y), inverse=True)
ur_lon, ur_lat = prj(max(x), max(y), inverse=True)
return Basemap(projection='stere', lat_0=lat_0, lon_0=lon_0,
llcrnrlon=ll_lon, llcrnrlat=ll_lat,
urcrnrlon=ur_lon, urcrnrlat=ur_lat, **kwargs)
llcrnrlon=-100
urcrnrlon=-30
llcrnrlat=-90
urcrnrlat=-55.0
m = polar_stere(llcrnrlon, urcrnrlon, llcrnrlat, urcrnrlat)
m.drawmeridians(np.arange(0,360,30),labels=[1,1,1,0])
m.drawparallels(np.arange(-90,90,30),labels=[1,1,1,1])
m.drawcoastlines()
plt.show()
