diff --git a/lib/cartopy/crs.py b/lib/cartopy/crs.py
index 2fa1a2d90..f193cbda2 100644
--- a/lib/cartopy/crs.py
+++ b/lib/cartopy/crs.py
@@ -841,9 +841,17 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
                 proj4_params += [('approx', None)]
         super().__init__(proj4_params, globe=globe)
 
+        # TODO: Let the globe return the semimajor axis always.
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        b = np.float(self.globe.semiminor_axis or a)
+
+        self._x_limits = (-np.pi * a, np.pi * a)
+        self._y_limits = (-np.pi / 2 * b, np.pi / 2 * b)
+        self._threshold = min(a, b) * 1.5e-3  # Approximately 1e4 for defaults.
+
     @property
     def threshold(self):
-        return 1e4
+        return self._threshold
 
     @property
     def boundary(self):
@@ -855,11 +863,11 @@ def boundary(self):
 
     @property
     def x_limits(self):
-        return (-2e7, 2e7)
+        return self._x_limits
 
     @property
     def y_limits(self):
-        return (-1e7, 1e7)
+        return self._y_limits
 
 
 class OSGB(TransverseMercator):
@@ -1641,9 +1649,15 @@ def __init__(self, central_longitude=0, false_easting=None,
                          false_northing=false_northing,
                          globe=globe)
 
+        # TODO: Let the globe return the semimajor axis always.
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        b = np.float(self.globe.semiminor_axis or a)
+
+        self._threshold = min(a, b) / 63.78137  # About 1e5 for defaults.
+
     @property
     def threshold(self):
-        return 1e5
+        return self._threshold
 
 
 class EckertI(_Eckert):
@@ -1813,9 +1827,15 @@ def __init__(self, central_longitude=0, globe=None,
                          false_northing=false_northing,
                          globe=globe)
 
+        # TODO: Let the globe return the semimajor axis always.
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        b = np.float(self.globe.semiminor_axis or a)
+
+        self._threshold = min(a, b) / 63.78137  # About 1e5 for defaults.
+
     @property
     def threshold(self):
-        return 1e5
+        return self._threshold
 
 
 class Robinson(_WarpedRectangularProjection):
@@ -2309,6 +2329,7 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
         maxs = np.max(coords, axis=1)
         self._x_limits = mins[0], maxs[0]
         self._y_limits = mins[1], maxs[1]
+        self._threshold = min(a, b) * 1.5e-3  # Approximately 1e4 for defaults.
 
     @property
     def boundary(self):
@@ -2316,7 +2337,7 @@ def boundary(self):
 
     @property
     def threshold(self):
-        return 1e5
+        return self._threshold
 
     @property
     def x_limits(self):
diff --git a/lib/cartopy/tests/crs/test_transverse_mercator.py b/lib/cartopy/tests/crs/test_transverse_mercator.py
index 3b35d038d..56540714f 100644
--- a/lib/cartopy/tests/crs/test_transverse_mercator.py
+++ b/lib/cartopy/tests/crs/test_transverse_mercator.py
@@ -12,6 +12,7 @@
 import pytest
 
 import cartopy.crs as ccrs
+from .helpers import check_proj_params
 
 
 @pytest.mark.parametrize('approx', [True, False])
@@ -21,16 +22,56 @@ def setup_class(self):
         self.point_b = (0.5, 50.5)
         self.src_crs = ccrs.PlateCarree()
 
+    def check_args(self, approx, proj, other_args):
+        if ccrs.PROJ4_VERSION < (6, 0, 0):
+            other_args = {*other_args, 'lon_0=0.0', 'lat_0=0.0', 'k=1.0',
+                          'x_0=0.0', 'y_0=0.0', 'units=m'}
+            check_proj_params('tmerc' if approx else 'etmerc', proj,
+                              other_args)
+        else:
+            other_args = {*other_args, 'lon_0=0.0', 'lat_0=0.0', 'k=1.0',
+                          'x_0=0.0', 'y_0=0.0', 'units=m'}
+            if approx:
+                other_args.add('approx')
+            check_proj_params('tmerc', proj, other_args)
+
     def test_default(self, approx):
         proj = ccrs.TransverseMercator(approx=approx)
+        self.check_args(approx, proj, {'ellps=WGS84'})
+
+        np.testing.assert_array_almost_equal(proj.x_limits, (-2e7, 2e7),
+                                             decimal=-5)
+        np.testing.assert_array_almost_equal(proj.y_limits, (-1e7, 1e7),
+                                             decimal=-5)
+
         res = proj.transform_point(*self.point_a, src_crs=self.src_crs)
         np.testing.assert_array_almost_equal(res,
                                              (-245269.53181, 5627508.74355),
                                              decimal=5)
+
         res = proj.transform_point(*self.point_b, src_crs=self.src_crs)
         np.testing.assert_array_almost_equal(res, (35474.63566645,
                                                    5596583.41949901))
 
+    def test_sphere_globe(self, approx):
+        if not approx:
+            pytest.skip('Not supported by proj.')
+
+        globe = ccrs.Globe(semimajor_axis=1000, ellipse=None)
+        proj = ccrs.TransverseMercator(approx=approx, globe=globe)
+        self.check_args(approx, proj, {'a=1000'})
+
+        np.testing.assert_array_almost_equal(proj.x_limits,
+                                             (-3141.592654, 3141.592654))
+        np.testing.assert_array_almost_equal(proj.y_limits,
+                                             (-1570.796327, 1570.796327))
+
+        res = proj.transform_point(*self.point_a, src_crs=self.src_crs)
+        np.testing.assert_array_almost_equal(res, (-38.377488, 886.259630))
+
+        res = proj.transform_point(*self.point_b, src_crs=self.src_crs)
+        np.testing.assert_array_almost_equal(res, (5.550816, 881.409961))
+
     def test_osgb_vals(self, approx):
         proj = ccrs.TransverseMercator(central_longitude=-2,
                                        central_latitude=49,