diff --git a/tests/test_runs/test_run_functions.py b/tests/test_runs/test_run_functions.py
index cb5d5e59d..b61477075 100644
--- a/tests/test_runs/test_run_functions.py
+++ b/tests/test_runs/test_run_functions.py
@@ -223,7 +223,9 @@ def _assert_predictions_equal(self, predictions, predictions_prime):
     def _rerun_model_and_compare_predictions(self, run_id, model_prime, seed, create_task_obj):
         run = openml.runs.get_run(run_id)
 
-        # TODO: assert holdout task
+        # assert for holdout task
+        task = openml.tasks.get_task(run.task_id)
+        assert task.estimation_procedure["type"] == "holdout"
 
         # downloads the predictions of the old task
         file_id = run.output_files["predictions"]
@@ -340,12 +342,20 @@ def _remove_random_state(flow):
         assert isinstance(run.dataset_id, int)
 
         # This is only a smoke check right now
-        # TODO add a few asserts here
         run._to_xml()
+        assert isinstance(run._to_xml(), str)
+
         if run.trace is not None:
             # This is only a smoke check right now
-            # TODO add a few asserts here
+            assert run.trace.run_id == run.run_id
+            assert run.trace.trace_iterations is not None
+            for trace_iteration in run.trace.trace_iterations.values():
+                assert (trace_iteration.setup_string is not None) != (
+                    trace_iteration.parameters is not None
+                )
+
             run.trace.trace_to_arff()
+            assert isinstance(run.trace, dict)
 
         # check arff output
         assert len(run.data_content) == num_instances
@@ -391,13 +401,18 @@ def _remove_random_state(flow):
 
         downloaded = openml.runs.get_run(run_.run_id)
         assert "openml-python" in downloaded.tags
-
         # TODO make sure that these attributes are instantiated when
         # downloading a run? Or make sure that the trace object is created when
         # running a flow on a task (and not only the arff object is created,
         # so that the two objects can actually be compared):
-        # downloaded_run_trace = downloaded._generate_trace_arff_dict()  # noqa: ERA001
-        # self.assertEqual(run_trace, downloaded_run_trace)  # noqa: ERA001
+        # downloaded_run_trace = downloaded._generate_trace_arff_dict()
+        # self.assertEqual(run_trace, downloaded_run_trace)
+
+        downloaded_run_trace = downloaded.trace
+        assert downloaded_run_trace is not None
+        assert run.trace is not None
+        assert run.trace == downloaded_run_trace
+
         return run
 
     def _check_sample_evaluations(