diff --git a/maint_tools/test_docstrings.py b/maint_tools/test_docstrings.py
index 587190401c61e..7a6ac7777cb39 100644
--- a/maint_tools/test_docstrings.py
+++ b/maint_tools/test_docstrings.py
@@ -24,7 +24,6 @@
     "DummyClassifier",
     "ElasticNetCV",
     "EllipticEnvelope",
-    "EmpiricalCovariance",
     "ExtraTreeClassifier",
     "ExtraTreeRegressor",
     "ExtraTreesClassifier",
diff --git a/sklearn/covariance/_empirical_covariance.py b/sklearn/covariance/_empirical_covariance.py
index 4ffab8af5ceea..34193166dc928 100644
--- a/sklearn/covariance/_empirical_covariance.py
+++ b/sklearn/covariance/_empirical_covariance.py
@@ -99,7 +99,7 @@ def empirical_covariance(X, *, assume_centered=False):
 
 
 class EmpiricalCovariance(BaseEstimator):
-    """Maximum likelihood covariance estimator
+    """Maximum likelihood covariance estimator.
 
     Read more in the :ref:`User Guide <covariance>`.
 
@@ -131,6 +131,18 @@ class EmpiricalCovariance(BaseEstimator):
 
         .. versionadded:: 0.24
 
+    See Also
+    --------
+    EllipticEnvelope : An object for detecting outliers in
+        a Gaussian distributed dataset.
+    GraphicalLasso : Sparse inverse covariance estimation
+        with an l1-penalized estimator.
+    LedoitWolf : LedoitWolf Estimator.
+    MinCovDet : Minimum Covariance Determinant
+        (robust estimator of covariance).
+    OAS : Oracle Approximating Shrinkage Estimator.
+    ShrunkCovariance : Covariance estimator with shrinkage.
+
     Examples
     --------
     >>> import numpy as np
@@ -148,7 +160,6 @@ class EmpiricalCovariance(BaseEstimator):
            [0.2818..., 0.3928...]])
     >>> cov.location_
     array([0.0622..., 0.0193...])
-
     """
 
     def __init__(self, *, store_precision=True, assume_centered=False):
@@ -191,8 +202,7 @@ def get_precision(self):
         return precision
 
     def fit(self, X, y=None):
-        """Fits the Maximum Likelihood Estimator covariance model
-        according to the given training data and parameters.
+        """Fit the maximum liklihood covariance estimator to X.
 
         Parameters
         ----------
@@ -206,6 +216,7 @@ def fit(self, X, y=None):
         Returns
         -------
         self : object
+            Returns the instance itself.
         """
         X = self._validate_data(X)
         if self.assume_centered: