diff --git a/providers/standard/src/airflow/providers/standard/operators/datetime.py b/providers/standard/src/airflow/providers/standard/operators/datetime.py
index 589e106fe31ba..26f90efe14008 100644
--- a/providers/standard/src/airflow/providers/standard/operators/datetime.py
+++ b/providers/standard/src/airflow/providers/standard/operators/datetime.py
@@ -71,10 +71,16 @@ def __init__(
 
     def choose_branch(self, context: Context) -> str | Iterable[str]:
         if self.use_task_logical_date:
-            now = context.get("logical_date")
-            if not now:
-                dag_run = context.get("dag_run")
-                now = dag_run.run_after  # type: ignore[union-attr, assignment]
+            logical_date = context.get("logical_date")
+            dag_run = context.get("dag_run")
+
+            if not (logical_date or (dag_run and dag_run.run_after)):
+                raise ValueError(
+                    "Either `logical_date` or `run_after` should be provided in the task context when "
+                    "`use_task_logical_date` is True"
+                )
+
+            now = logical_date or dag_run.run_after  # type: ignore[union-attr]
         else:
             now = timezone.coerce_datetime(timezone.utcnow())
         if TYPE_CHECKING:
@@ -111,4 +117,4 @@ def target_times_as_dates(
 
     if upper < lower:
         upper += datetime.timedelta(days=1)
-    return lower, upper
+    return lower, upper
\ No newline at end of file
diff --git a/providers/standard/src/airflow/providers/standard/operators/weekday.py b/providers/standard/src/airflow/providers/standard/operators/weekday.py
index e663bc7e4f0f1..0012755b3f917 100644
--- a/providers/standard/src/airflow/providers/standard/operators/weekday.py
+++ b/providers/standard/src/airflow/providers/standard/operators/weekday.py
@@ -111,13 +111,19 @@ def __init__(
 
     def choose_branch(self, context: Context) -> str | Iterable[str]:
         if self.use_task_logical_date:
-            now = context.get("logical_date")
-            if not now:
-                dag_run = context.get("dag_run")
-                now = dag_run.run_after  # type: ignore[union-attr, assignment]
+            logical_date = context.get("logical_date")
+            dag_run = context.get("dag_run")
+
+            if not (logical_date or (dag_run and dag_run.run_after)):
+                raise ValueError(
+                    "Either `logical_date` or `run_after` should be provided in the task context when "
+                    "`use_task_logical_date` is True"
+                )
+
+            now = logical_date or dag_run.run_after  # type: ignore[union-attr]
         else:
             now = timezone.make_naive(timezone.utcnow(), self.dag.timezone)
 
         if now.isoweekday() in self._week_day_num:  # type: ignore[union-attr]
             return self.follow_task_ids_if_true
-        return self.follow_task_ids_if_false
+        return self.follow_task_ids_if_false
\ No newline at end of file
diff --git a/providers/standard/tests/unit/standard/operators/test_datetime.py b/providers/standard/tests/unit/standard/operators/test_datetime.py
index c9e38e6c9602f..78cca83f27f1b 100644
--- a/providers/standard/tests/unit/standard/operators/test_datetime.py
+++ b/providers/standard/tests/unit/standard/operators/test_datetime.py
@@ -344,3 +344,32 @@ def test_choose_branch_should_use_run_after_when_logical_date_none(self, dag_mak
             **{"run_after": timezone.datetime(2020, 8, 7)},
         )
         assert branch_op.choose_branch(context={"dag_run": dr}) == "branch_1"
+
+    @pytest.mark.skipif(not AIRFLOW_V_3_0_PLUS, reason="Skip on Airflow < 3.0")
+    @time_machine.travel("2020-12-01 09:00:00")
+    def test_choose_branch_should_raise_when_neither_logical_date_nor_run_after(self, dag_maker):
+        with dag_maker(
+            "branch_datetime_operator_raises_without_date",
+            default_args={"owner": "airflow", "start_date": DEFAULT_DATE},
+            schedule=INTERVAL,
+            serialized=True,
+        ):
+            branch_1 = EmptyOperator(task_id="branch_1")
+            branch_2 = EmptyOperator(task_id="branch_2")
+
+            branch_op = BranchDateTimeOperator(
+                task_id="datetime_branch",
+                follow_task_ids_if_true="branch_1",
+                follow_task_ids_if_false="branch_2",
+                target_upper=datetime.datetime(2020, 9, 7, 11, 0, 0),
+                target_lower=datetime.datetime(2020, 6, 7, 10, 0, 0),
+                use_task_logical_date=True,
+            )
+            branch_1.set_upstream(branch_op)
+            branch_2.set_upstream(branch_op)
+
+        with pytest.raises(
+            ValueError,
+            match="Either `logical_date` or `run_after` should be provided in the task context",
+        ):
+            branch_op.choose_branch(context={})
diff --git a/providers/standard/tests/unit/standard/operators/test_weekday.py b/providers/standard/tests/unit/standard/operators/test_weekday.py
index 957c94e7295ef..636b57e713030 100644
--- a/providers/standard/tests/unit/standard/operators/test_weekday.py
+++ b/providers/standard/tests/unit/standard/operators/test_weekday.py
@@ -206,6 +206,30 @@ def test_choose_branch_should_use_run_after_when_logical_date_none(self, dag_mak
         )
         assert branch_op.choose_branch(context={"dag_run": dr}) == "branch_1"
 
+    @pytest.mark.skipif(not AIRFLOW_V_3_0_PLUS, reason="Skip on Airflow < 3.0")
+    @time_machine.travel("2021-01-25")  # Monday
+    def test_choose_branch_should_raise_when_neither_logical_date_nor_run_after(self, dag_maker):
+        with dag_maker(
+            "branch_day_of_week_operator_test", start_date=DEFAULT_DATE, schedule=INTERVAL, serialized=True
+        ):
+            branch_op = BranchDayOfWeekOperator(
+                task_id="make_choice",
+                follow_task_ids_if_true="branch_1",
+                follow_task_ids_if_false="branch_2",
+                week_day="Wednesday",
+                use_task_logical_date=True,
+            )
+            branch_1 = EmptyOperator(task_id="branch_1")
+            branch_2 = EmptyOperator(task_id="branch_2")
+            branch_1.set_upstream(branch_op)
+            branch_2.set_upstream(branch_op)
+
+        with pytest.raises(
+            ValueError,
+            match="Either `logical_date` or `run_after` should be provided in the task context",
+        ):
+            branch_op.choose_branch(context={})
+
     @time_machine.travel("2021-01-25")  # Monday
     def test_branch_follow_false(self, dag_maker):
         """Checks if BranchDayOfWeekOperator follow false branch"""