diff --git a/py/selenium/webdriver/remote/switch_to.py b/py/selenium/webdriver/remote/switch_to.py
index 30a26ed760f39..26772f2c48263 100644
--- a/py/selenium/webdriver/remote/switch_to.py
+++ b/py/selenium/webdriver/remote/switch_to.py
@@ -80,13 +80,14 @@ def frame(self, frame_reference: Union[str, int, WebElement]) -> None:
                 driver.switch_to.frame(driver.find_elements(By.TAG_NAME, "iframe")[0])
         """
         if isinstance(frame_reference, str):
+            frame_name = frame_reference
             try:
                 frame_reference = self._driver.find_element(By.ID, frame_reference)
             except NoSuchElementException:
                 try:
                     frame_reference = self._driver.find_element(By.NAME, frame_reference)
                 except NoSuchElementException as exc:
-                    raise NoSuchFrameException(frame_reference) from exc
+                    raise NoSuchFrameException(frame_name) from exc
 
         self._driver.execute(Command.SWITCH_TO_FRAME, {"id": frame_reference})
 
diff --git a/py/selenium/webdriver/support/relative_locator.py b/py/selenium/webdriver/support/relative_locator.py
index 5962ae128c874..9022331838839 100644
--- a/py/selenium/webdriver/support/relative_locator.py
+++ b/py/selenium/webdriver/support/relative_locator.py
@@ -18,7 +18,7 @@
 from typing import NoReturn, Optional, Union, overload
 
 from selenium.common.exceptions import WebDriverException
-from selenium.webdriver.common.by import By, ByType
+from selenium.webdriver.common.by import ByType
 from selenium.webdriver.remote.webelement import WebElement
 
 
@@ -48,7 +48,7 @@ def with_tag_name(tag_name: str) -> "RelativeBy":
     warnings.warn("This method is deprecated and may be removed in future versions. Please use `locate_with` instead.")
     if not tag_name:
         raise WebDriverException("tag_name can not be null")
-    return RelativeBy({By.CSS_SELECTOR: tag_name})
+    return RelativeBy({"css selector": tag_name})
 
 
 def locate_with(by: ByType, using: str) -> "RelativeBy":