diff --git a/packages/@ember/-internals/container/lib/container.ts b/packages/@ember/-internals/container/lib/container.ts
index 3647776e505..546b85fe351 100644
--- a/packages/@ember/-internals/container/lib/container.ts
+++ b/packages/@ember/-internals/container/lib/container.ts
@@ -7,7 +7,7 @@ import type {
   FullName,
 } from '@ember/-internals/owner';
 import { setOwner } from '@ember/-internals/owner';
-import { dictionary } from '@ember/-internals/utils';
+import { dictionary, guidFor } from '@ember/-internals/utils';
 import { assert } from '@ember/debug';
 import { DEBUG } from '@glimmer/env';
 import type { DebugRegistry } from './registry';
@@ -152,7 +152,20 @@ export default class Container {
     options?: RegisterOptions
   ): InternalFactory<object> | object | undefined {
     if (this.isDestroyed) {
-      throw new Error(`Cannot call \`.lookup('${fullName}')\` after the owner has been destroyed`);
+      if (macroCondition(isTesting())) {
+        let guid = guidFor(this.owner);
+        // SAFETY: cast is for accessing private data stored globally
+        let testInfo = (globalThis as any)['__OWNER_MAP__']?.get(guid);
+
+        throw new Error(
+          `Cannot call \`.lookup('${fullName}')\` after the owner has been destroyed. ` +
+            `owner is ${guid} (test ${testInfo?.testId} ${testInfo?.name})`
+        );
+      } else {
+        throw new Error(
+          `Cannot call \`.lookup('${fullName}')\` after the owner has been destroyed`
+        );
+      }
     }
     assert('fullName must be a proper full name', this.registry.isValidFullName(fullName));
     return lookup(this, this.registry.normalize(fullName), options);
diff --git a/packages/@ember/-internals/metal/lib/property_set.ts b/packages/@ember/-internals/metal/lib/property_set.ts
index 65b78f9c1ed..55e6f1958a2 100644
--- a/packages/@ember/-internals/metal/lib/property_set.ts
+++ b/packages/@ember/-internals/metal/lib/property_set.ts
@@ -1,4 +1,10 @@
-import { lookupDescriptor, setWithMandatorySetter, toString } from '@ember/-internals/utils';
+import { getOwner } from '@ember/-internals/owner';
+import {
+  guidFor,
+  lookupDescriptor,
+  setWithMandatorySetter,
+  toString,
+} from '@ember/-internals/utils';
 import { assert } from '@ember/debug';
 import { DEBUG } from '@glimmer/env';
 import { COMPUTED_SETTERS } from './decorator';
@@ -55,10 +61,23 @@ export function set<T>(obj: object, keyName: string, value: T, tolerant?: boolea
   );
 
   if ((obj as ExtendedObject).isDestroyed) {
-    assert(
-      `calling set on destroyed object: ${toString(obj)}.${keyName} = ${toString(value)}`,
-      tolerant
-    );
+    if (macroCondition(isTesting())) {
+      let guid = guidFor(getOwner(obj));
+
+      // SAFETY: cast is for accessing private data stored globally
+      let testInfo = (globalThis as any)['__OWNER_MAP__']?.get(guid);
+      assert(
+        `calling set on destroyed object: ${toString(obj)}.${keyName} = ${toString(value)} ` +
+          `owner is ${guid} (test ${testInfo?.testId} ${testInfo?.name})`,
+        tolerant
+      );
+    } else {
+      assert(
+        `calling set on destroyed object: ${toString(obj)}.${keyName} = ${toString(value)}`,
+        tolerant
+      );
+    }
+
     return value;
   }