diff --git a/SysML2.NET.Tests/Extend/ElementExtensionsTestFixture.cs b/SysML2.NET.Tests/Extend/ElementExtensionsTestFixture.cs
index 11f56051..706a8d2b 100644
--- a/SysML2.NET.Tests/Extend/ElementExtensionsTestFixture.cs
+++ b/SysML2.NET.Tests/Extend/ElementExtensionsTestFixture.cs
@@ -289,17 +289,17 @@ public void VerifyComputePathOperation()
             using (Assert.EnterMultipleScope())
             {
                 Assert.That(element.ComputePathOperation, Is.EqualTo("name"));
-                Assert.That(secondElement.ComputePathOperation, Throws.TypeOf<NotSupportedException>());
+                Assert.That(secondElement.ComputePathOperation(), Is.EqualTo("/2/1"));
             }
-            
+
             namespaceElement.DeclaredName = "namespace";
             membership.DeclaredName = "firstMember";
             secondMembership.DeclaredName = "secondMember";
-            
+
             using (Assert.EnterMultipleScope())
             {
                 Assert.That(element.ComputePathOperation, Is.EqualTo("name"));
-                Assert.That(secondElement.ComputePathOperation, Throws.TypeOf<NotSupportedException>());
+                Assert.That(secondElement.ComputePathOperation(), Is.EqualTo("/2/1"));
             }
         }
 
diff --git a/SysML2.NET.Tests/Extend/OwningMembershipExtensionsTestFixture.cs b/SysML2.NET.Tests/Extend/OwningMembershipExtensionsTestFixture.cs
index ac6ec88d..e50d0069 100644
--- a/SysML2.NET.Tests/Extend/OwningMembershipExtensionsTestFixture.cs
+++ b/SysML2.NET.Tests/Extend/OwningMembershipExtensionsTestFixture.cs
@@ -57,9 +57,22 @@ public void VerifyComputeOwnedMemberElement()
         }
 
         [Test]
-        public void ComputeOwnedMemberElementId_ThrowsNotSupportedException()
+        public void VerifyComputeOwnedMemberElementId()
         {
-            Assert.That(() => ((IOwningMembership)null).ComputeOwnedMemberElementId(), Throws.TypeOf<NotSupportedException>());
+            Assert.That(() => ((IOwningMembership)null).ComputeOwnedMemberElementId(), Throws.TypeOf<ArgumentNullException>());
+
+            // OwnedRelatedElement.Count != 1 → IncompleteModelException propagated from ComputeOwnedMemberElement
+            var emptyMembership = new OwningMembership();
+
+            Assert.That(() => emptyMembership.ComputeOwnedMemberElementId(), Throws.TypeOf<IncompleteModelException>());
+
+            // Populated: one owned element → returns that element's ElementId
+            var container = new Namespace();
+            var membership = new OwningMembership();
+            var ownedElement = new Definition { ElementId = "test-element-id-42" };
+            container.AssignOwnership(membership, ownedElement);
+
+            Assert.That(membership.ComputeOwnedMemberElementId(), Is.EqualTo(ownedElement.ElementId));
         }
 
         [Test]
@@ -73,5 +86,40 @@ public void ComputeOwnedMemberShortName_ThrowsArgumentNullException()
         {
             Assert.That(() => ((IOwningMembership)null).ComputeOwnedMemberShortName(), Throws.TypeOf<ArgumentNullException>());
         }
+
+        [Test]
+        public void VerifyComputeRedefinedPathOperation()
+        {
+            Assert.That(() => ((IOwningMembership)null).ComputeRedefinedPathOperation(), Throws.TypeOf<ArgumentNullException>());
+
+            // OwnedRelatedElement.Count != 1 → IncompleteModelException propagated from ComputeOwnedMemberElement
+            var emptyMembership = new OwningMembership();
+
+            Assert.That(() => emptyMembership.ComputeRedefinedPathOperation(), Throws.TypeOf<IncompleteModelException>());
+
+            // qualifiedName != null → returns qualifiedName + "/owningMembership"
+            // Wire: owning package → named child namespace → named member definition
+            var rootPackage = new Namespace();
+            var childNamespace = new Namespace { DeclaredName = "Pkg" };
+            var childMembership = new OwningMembership();
+            rootPackage.AssignOwnership(childMembership, childNamespace);
+
+            var member = new Definition { DeclaredName = "Member" };
+            var memberMembership = new OwningMembership();
+            childNamespace.AssignOwnership(memberMembership, member);
+
+            Assert.That(memberMembership.ComputeRedefinedPathOperation(), Is.EqualTo("Pkg::Member/owningMembership"));
+
+            // qualifiedName == null → delegates to RelationshipExtensions.ComputeRedefinedPathOperation
+            // Wire: an OwningMembership with an unnamed owned element (no owning namespace → qualifiedName is null)
+            var unnamedContainer = new Namespace();
+            var unnamedMembership = new OwningMembership();
+            var unnamedElement = new Definition();
+            unnamedContainer.AssignOwnership(unnamedMembership, unnamedElement);
+
+            var expectedPath = ((IRelationship)unnamedMembership).ComputeRedefinedPathOperation();
+
+            Assert.That(unnamedMembership.ComputeRedefinedPathOperation(), Is.EqualTo(expectedPath));
+        }
     }
 }
diff --git a/SysML2.NET/Extend/OwningMembershipExtensions.cs b/SysML2.NET/Extend/OwningMembershipExtensions.cs
index acba5948..b28d15e7 100644
--- a/SysML2.NET/Extend/OwningMembershipExtensions.cs
+++ b/SysML2.NET/Extend/OwningMembershipExtensions.cs
@@ -62,10 +62,9 @@ internal static IElement ComputeOwnedMemberElement(this IOwningMembership owning
         /// <returns>
         /// the computed result
         /// </returns>
-        [System.Diagnostics.CodeAnalysis.ExcludeFromCodeCoverage]
         internal static string ComputeOwnedMemberElementId(this IOwningMembership owningMembershipSubject)
         {
-            throw new NotSupportedException("Create a GitHub issue when this method is required");
+            return owningMembershipSubject == null ? throw new ArgumentNullException(nameof(owningMembershipSubject)) : owningMembershipSubject.ownedMemberElement.ElementId;
         }
 
         /// <summary>
@@ -119,10 +118,21 @@ internal static string ComputeOwnedMemberShortName(this IOwningMembership owning
         /// <returns>
         /// The expected <see cref="string" />
         /// </returns>
-        [System.Diagnostics.CodeAnalysis.ExcludeFromCodeCoverage]
         internal static string ComputeRedefinedPathOperation(this IOwningMembership owningMembershipSubject)
         {
-            throw new NotSupportedException("Create a GitHub issue when this method is required");
+            if (owningMembershipSubject == null)
+            {
+                throw new ArgumentNullException(nameof(owningMembershipSubject));
+            }
+
+            var ownedElement = owningMembershipSubject.ownedMemberElement;
+
+            if (ownedElement.qualifiedName != null)
+            {
+                return $"{ownedElement.qualifiedName}/owningMembership";
+            }
+
+            return RelationshipExtensions.ComputeRedefinedPathOperation(owningMembershipSubject);
         }
     }
 }