diff --git a/tests/pytests/integration/cli/test_batch.py b/tests/pytests/integration/cli/test_batch.py
index 230aa6d5cbb2..f5b104ba67b1 100644
--- a/tests/pytests/integration/cli/test_batch.py
+++ b/tests/pytests/integration/cli/test_batch.py
@@ -179,7 +179,19 @@ def test_batch_retcode(salt_cli, salt_minion, salt_sub_minion, run_timeout):
     )
 
     assert cmd.returncode == 23
-    assert not cmd.stderr
+    # TODO: Certain platforms will have a warning related to jinja. But
+    # that's an issue with dependency versions that may be due to the versions
+    # installed on the test images. When those issues are sorted, this can
+    # simply `not cmd.stderr`.
+    assert (
+        not cmd.stderr
+        or cmd.stderr.endswith(
+            "jinja.py:736: DeprecationWarning: 'contextfunction' is renamed to 'pass_context', the old name will be removed in Jinja 3.1.\n  @contextfunction\n"
+        )
+        or cmd.stderr.endswith(
+            "process.py:54: DeprecationWarning: PY_SSIZE_T_CLEAN will be required for '#' formats\n  current = setproctitle.getproctitle()\n"
+        )
+    )
     assert "true" in cmd.stdout
 
 
@@ -198,7 +210,19 @@ def test_multiple_modules_in_batch(salt_cli, salt_minion, salt_sub_minion, run_t
     )
 
     assert cmd.returncode == 23
-    assert not cmd.stderr
+    # TODO: Certain platforms will have a warning related to setproctitle. But
+    # that's an issue with dependency versions that may be due to the versions
+    # installed on the test images. When those issues are sorted, this can
+    # simply `not cmd.stderr`.
+    assert (
+        not cmd.stderr
+        or cmd.stderr.endswith(
+            "process.py:54: DeprecationWarning: PY_SSIZE_T_CLEAN will be required for '#' formats\n  current = setproctitle.getproctitle()\n"
+        )
+        or cmd.stderr.endswith(
+            "jinja.py:736: DeprecationWarning: 'contextfunction' is renamed to 'pass_context', the old name will be removed in Jinja 3.1.\n  @contextfunction\n"
+        )
+    )
 
 
 def test_batch_module_stopping_failed_respond(
diff --git a/tests/pytests/scenarios/daemons/test_salt_as_daemons.py b/tests/pytests/scenarios/daemons/test_salt_as_daemons.py
index e4dca82ce6ac..4769f261cdac 100644
--- a/tests/pytests/scenarios/daemons/test_salt_as_daemons.py
+++ b/tests/pytests/scenarios/daemons/test_salt_as_daemons.py
@@ -24,7 +24,28 @@ def test_salt_master_as_daemon(salt_master_factory):
             pass
         finally:
             assert salt_master_factory.impl._terminal_result.stdout == ""
-            assert salt_master_factory.impl._terminal_result.stderr == ""
+            # TODO currently setproctitle.getproctitle warns on some platforms.
+            # It's fine, actually, for that warning to show up, until the
+            # correct versions are configured for those platforms. When they
+            # are, the 'if not all(...):' line should be removed and just the
+            # assertion that `stderr == ""` should be left.
+            if not any(
+                (
+                    all(
+                        text in salt_master_factory.impl._terminal_result.stderr
+                        for text in ("PY_SSIZE_T_CLEAN", "salt/utils/process.py:54")
+                    ),
+                    all(
+                        text in salt_master_factory.impl._terminal_result.stderr
+                        for text in (
+                            "salt/utils/jinja.py:736",
+                            "contextfunction",
+                            "pass_context",
+                        )
+                    ),
+                )
+            ):
+                assert salt_master_factory.impl._terminal_result.stderr == ""
             assert salt_master_factory.impl._terminal_result.returncode == 0
 
             # We are going to kill the possible child processes based on the entire cmdline
@@ -61,7 +82,28 @@ def test_salt_minion_as_daemon(salt_minion_factory):
             pass
         finally:
             assert salt_minion_factory.impl._terminal_result.stdout == ""
-            assert salt_minion_factory.impl._terminal_result.stderr == ""
+            # TODO currently setproctitle.getproctitle warns on some platforms.
+            # It's fine, actually, for that warning to show up, until the
+            # correct versions are configured for those platforms. When they
+            # are, the 'if not all(...):' line should be removed and just the
+            # assertion that `stderr == ""` should be left.
+            if not any(
+                (
+                    all(
+                        text in salt_minion_factory.impl._terminal_result.stderr
+                        for text in ("PY_SSIZE_T_CLEAN", "salt/utils/process.py:54")
+                    ),
+                    all(
+                        text in salt_minion_factory.impl._terminal_result.stderr
+                        for text in (
+                            "salt/utils/jinja.py:736",
+                            "contextfunction",
+                            "pass_context",
+                        )
+                    ),
+                )
+            ):
+                assert salt_minion_factory.impl._terminal_result.stderr == ""
             assert salt_minion_factory.impl._terminal_result.returncode == 0
 
             # We are going to kill the possible child processes based on the entire cmdline