diff --git a/src/werkzeug/routing/exceptions.py b/src/werkzeug/routing/exceptions.py
index eeabd4ed1..1cf24ceb7 100644
--- a/src/werkzeug/routing/exceptions.py
+++ b/src/werkzeug/routing/exceptions.py
@@ -34,9 +34,10 @@ class RequestRedirect(HTTPException, RoutingException):
 
     code = 308
 
-    def __init__(self, new_url: str) -> None:
+    def __init__(self, new_url: str, new_path: t.Optional[str] = None) -> None:
         super().__init__(new_url)
         self.new_url = new_url
+        self.new_path = new_path
 
     def get_response(
         self,
@@ -98,7 +99,8 @@ def _score_rule(rule: Rule) -> float:
                         str(rule.endpoint),
                         str(self.endpoint),
                     ).ratio(),
-                    0.01 * bool(set(self.values or ()).issubset(rule.arguments)),
+                    0.01 * bool(set(self.values or ()
+                                    ).issubset(rule.arguments)),
                     0.01 * bool(rule.methods and self.method in rule.methods),
                 ]
             )
@@ -134,7 +136,8 @@ def __str__(self) -> str:
                         f" Did you forget to specify values {sorted(missing_values)!r}?"
                     )
             else:
-                message.append(f" Did you mean {self.suggested.endpoint!r} instead?")
+                message.append(
+                    f" Did you mean {self.suggested.endpoint!r} instead?")
         return "".join(message)
 
 
diff --git a/src/werkzeug/routing/map.py b/src/werkzeug/routing/map.py
index 4d15e8824..134b2da34 100644
--- a/src/werkzeug/routing/map.py
+++ b/src/werkzeug/routing/map.py
@@ -222,7 +222,8 @@ def bind(
         server_name = server_name.lower()
         if self.host_matching:
             if subdomain is not None:
-                raise RuntimeError("host matching enabled and a subdomain was provided")
+                raise RuntimeError(
+                    "host matching enabled and a subdomain was provided")
         elif subdomain is None:
             subdomain = self.default_subdomain
         if script_name is None:
@@ -602,12 +603,14 @@ def match(
         path_part = f"/{path_info.lstrip('/')}" if path_info else ""
 
         try:
-            result = self.map._matcher.match(domain_part, path_part, method, websocket)
+            result = self.map._matcher.match(
+                domain_part, path_part, method, websocket)
         except RequestPath as e:
             # safe = https://url.spec.whatwg.org/#url-path-segment-string
             new_path = quote(e.path_info, safe="!$&'()*+,/:;=@")
             raise RequestRedirect(
-                self.make_redirect_url(new_path, query_args)
+                self.make_redirect_url(new_path, query_args),
+                new_path,
             ) from None
         except RequestAliasRedirect as e:
             raise RequestRedirect(
@@ -617,11 +620,13 @@ def match(
                     e.matched_values,
                     method,
                     query_args,
-                )
+                ),
+                path_part,
             ) from None
         except NoMatch as e:
             if e.have_match_for:
-                raise MethodNotAllowed(valid_methods=list(e.have_match_for)) from None
+                raise MethodNotAllowed(
+                    valid_methods=list(e.have_match_for)) from None
 
             if e.websocket_mismatch:
                 raise WebsocketMismatch() from None
@@ -631,9 +636,10 @@ def match(
             rule, rv = result
 
             if self.map.redirect_defaults:
-                redirect_url = self.get_default_redirect(rule, method, rv, query_args)
+                (redirect_url, redirect_path) = self.get_default_redirect(
+                    rule, method, rv, query_args)
                 if redirect_url is not None:
-                    raise RequestRedirect(redirect_url)
+                    raise RequestRedirect(redirect_url, redirect_path)
 
             if rule.redirect_to is not None:
                 if isinstance(rule.redirect_to, str):
@@ -642,7 +648,8 @@ def _handle_match(match: t.Match[str]) -> str:
                         value = rv[match.group(1)]
                         return rule._converters[match.group(1)].to_url(value)
 
-                    redirect_url = _simple_rule_re.sub(_handle_match, rule.redirect_to)
+                    redirect_url = _simple_rule_re.sub(
+                        _handle_match, rule.redirect_to)
                 else:
                     redirect_url = rule.redirect_to(self, **rv)
 
@@ -655,7 +662,8 @@ def _handle_match(match: t.Match[str]) -> str:
                     urljoin(
                         f"{self.url_scheme or 'http'}://{netloc}{self.script_name}",
                         redirect_url,
-                    )
+                    ),
+                    redirect_url,
                 )
 
             if return_rule:
@@ -736,8 +744,9 @@ def get_default_redirect(
             if r.provides_defaults_for(rule) and r.suitable_for(values, method):
                 values.update(r.defaults)  # type: ignore
                 domain_part, path = r.build(values)  # type: ignore
-                return self.make_redirect_url(path, query_args, domain_part=domain_part)
-        return None
+                return self.make_redirect_url(path, query_args,
+                                              domain_part=domain_part), path
+        return None, None
 
     def encode_query_args(self, query_args: t.Mapping[str, t.Any] | str) -> str:
         if not isinstance(query_args, str):