diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3a0cb30a51..ecbc5dd4b5 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,7 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 - Fixed a crash in `TextArea` when undoing an edit to a selection the selection was made backwards https://github.com/Textualize/textual/issues/4301
 - Fixed issue with flickering scrollbars https://github.com/Textualize/textual/pull/4315
 - Fix progress bar ETA not updating when setting `total` reactive https://github.com/Textualize/textual/pull/4316
+- Exceptions inside `Widget.compose` or workers weren't bubbling up in tests https://github.com/Textualize/textual/issues/4282
 
 ### Changed 
 
diff --git a/src/textual/widget.py b/src/textual/widget.py
index aac76e8778..4bfaabdee0 100644
--- a/src/textual/widget.py
+++ b/src/textual/widget.py
@@ -3618,10 +3618,8 @@ async def _compose(self) -> None:
             raise TypeError(
                 f"{self!r} compose() method returned an invalid result; {error}"
             ) from error
-        except Exception:
-            from rich.traceback import Traceback
-
-            self.app.panic(Traceback())
+        except Exception as error:
+            self.app._handle_exception(error)
         else:
             self._extend_compose(widgets)
             await self.mount_composed_widgets(widgets)
diff --git a/src/textual/worker.py b/src/textual/worker.py
index 7719cd4dca..f7f10b60ae 100644
--- a/src/textual/worker.py
+++ b/src/textual/worker.py
@@ -375,7 +375,8 @@ async def _run(self, app: App) -> None:
 
             app.log.worker(Traceback())
             if self.exit_on_error:
-                app._fatal_error()
+                worker_failed = WorkerFailed(self._error)
+                app._handle_exception(worker_failed)
         else:
             self.state = WorkerState.SUCCESS
             app.log.worker(self)
diff --git a/tests/test_pilot.py b/tests/test_pilot.py
index d436f8b5fc..9451237fab 100644
--- a/tests/test_pilot.py
+++ b/tests/test_pilot.py
@@ -2,12 +2,14 @@
 
 import pytest
 
-from textual import events
+from textual import events, work
 from textual.app import App, ComposeResult
 from textual.binding import Binding
 from textual.containers import Center, Middle
 from textual.pilot import OutOfBounds
+from textual.screen import Screen
 from textual.widgets import Button, Label
+from textual.worker import WorkerFailed
 
 KEY_CHARACTERS_TO_TEST = "akTW03" + punctuation
 """Test some "simple" characters (letters + digits) and all punctuation."""
@@ -56,7 +58,7 @@ def on_key(self, event: events.Key) -> None:
             assert keys_pressed[-1] == char
 
 
-async def test_pilot_exception_catching_compose():
+async def test_pilot_exception_catching_app_compose():
     """Ensuring that test frameworks are aware of exceptions
     inside compose methods when running via Pilot run_test()."""
 
@@ -70,6 +72,21 @@ def compose(self) -> ComposeResult:
             pass
 
 
+async def test_pilot_exception_catching_widget_compose():
+    class SomeScreen(Screen[None]):
+        def compose(self) -> ComposeResult:
+            1 / 0
+            yield Label("Beep")
+
+    class FailingApp(App[None]):
+        def on_mount(self) -> None:
+            self.push_screen(SomeScreen())
+
+    with pytest.raises(ZeroDivisionError):
+        async with FailingApp().run_test():
+            pass
+
+
 async def test_pilot_exception_catching_action():
     """Ensure that exceptions inside action handlers are presented
     to the test framework when running via Pilot run_test()."""
@@ -85,6 +102,21 @@ def action_beep(self) -> None:
             await pilot.press("b")
 
 
+async def test_pilot_exception_catching_worker():
+    class SimpleAppThatCrashes(App[None]):
+        def on_mount(self) -> None:
+            self.crash()
+
+        @work(name="crash")
+        async def crash(self) -> None:
+            1 / 0
+
+    with pytest.raises(WorkerFailed) as exc:
+        async with SimpleAppThatCrashes().run_test():
+            pass
+        assert exc.type is ZeroDivisionError
+
+
 async def test_pilot_click_screen():
     """Regression test for https://github.com/Textualize/textual/issues/3395.
 
diff --git a/tests/workers/test_worker.py b/tests/workers/test_worker.py
index 7b553d122f..61af91f638 100644
--- a/tests/workers/test_worker.py
+++ b/tests/workers/test_worker.py
@@ -113,10 +113,10 @@ class ErrorApp(App):
         pass
 
     app = ErrorApp()
-    async with app.run_test():
-        worker: Worker[str] = Worker(app, run_error)
-        worker._start(app)
-        with pytest.raises(WorkerFailed):
+    with pytest.raises(WorkerFailed):
+        async with app.run_test():
+            worker: Worker[str] = Worker(app, run_error)
+            worker._start(app)
             await worker.wait()
 
 
@@ -218,12 +218,12 @@ async def self_referential_work():
         await get_current_worker().wait()
 
     app = App()
-    async with app.run_test():
-        worker = Worker(app, self_referential_work)
-        worker._start(app)
-        with pytest.raises(WorkerFailed) as exc:
+    with pytest.raises(WorkerFailed) as exc:
+        async with app.run_test():
+            worker = Worker(app, self_referential_work)
+            worker._start(app)
             await worker.wait()
-            assert exc.type is DeadlockError
+        assert exc.type is DeadlockError
 
 
 async def test_wait_without_start():