For that you need to do some tweaks.
Instead of using colormap, which adds a new axes to plot the colormap scale, you would be better defining a plotting area to show the color map.
I modified you code a little bit in order to do so.
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
#-- Generate Data -----------------------------------------
# Using linspace so that the endpoint of 360 is included...
azimuths = np.radians(np.linspace(0, 360, 100))
zeniths = np.arange(0, 70, 10)
r, theta = np.meshgrid(zeniths, azimuths)
values1 = np.random.random((azimuths.size, zeniths.size))
values2 = np.random.random((azimuths.size, zeniths.size))
#-- Plot... ------------------------------------------------
fig, axs = plt.subplots(1, 2, figsize=(12,5),subplot_kw=dict(projection='polar'))
p1 = axs[0].contourf(theta, r, values1, 100)
p2 = axs[1].contourf(theta, r, values2, 100)
#-- obtaining the colormap limits
vmin,vmax = p2.get_clim()
#-- Defining a normalised scale
cNorm = mpl.colors.Normalize(vmin=vmin, vmax=vmax)
#-- Creating a new axes at the right side
ax3 = fig.add_axes([0.9, 0.1, 0.03, 0.8])
#-- Plotting the colormap in the created axes
cb1 = mpl.colorbar.ColorbarBase(ax3, norm=cNorm)
fig.subplots_adjust(left=0.05,right=0.85)
plt.show()
Hope it helps