diff --git a/httpx/_models.py b/httpx/_models.py
index 2cc86321a4..1148e11a23 100644
--- a/httpx/_models.py
+++ b/httpx/_models.py
@@ -71,7 +71,9 @@ def _normalize_header_key(key: str | bytes, encoding: str | None = None) -> byte
     return key if isinstance(key, bytes) else key.encode(encoding or "ascii")
 
 
-def _normalize_header_value(value: str | bytes, encoding: str | None = None) -> bytes:
+def _normalize_header_value(
+    value: str | bytes, encoding: str | None = None, name: str | bytes = ""
+) -> bytes:
     """
     Coerce str/bytes into a strictly byte-wise HTTP header value.
     """
@@ -79,7 +81,18 @@ def _normalize_header_value(value: str | bytes, encoding: str | None = None) ->
         return value
     if not isinstance(value, str):
         raise TypeError(f"Header value must be str or bytes, not {type(value)}")
-    return value.encode(encoding or "ascii")
+    try:
+        return value.encode(encoding or "ascii")
+    except UnicodeEncodeError as exc:
+        if name:
+            raise UnicodeEncodeError(
+                exc.encoding,
+                exc.object,
+                exc.start,
+                exc.end,
+                f"{exc.reason} (header: {name!r})",
+            ) from None
+        raise
 
 
 def _parse_content_type_charset(content_type: str) -> str | None:
@@ -153,12 +166,12 @@ def __init__(
         elif isinstance(headers, Mapping):
             for k, v in headers.items():
                 bytes_key = _normalize_header_key(k, encoding)
-                bytes_value = _normalize_header_value(v, encoding)
+                bytes_value = _normalize_header_value(v, encoding, name=k)
                 self._list.append((bytes_key, bytes_key.lower(), bytes_value))
         elif headers is not None:
             for k, v in headers:
                 bytes_key = _normalize_header_key(k, encoding)
-                bytes_value = _normalize_header_value(v, encoding)
+                bytes_value = _normalize_header_value(v, encoding, name=k)
                 self._list.append((bytes_key, bytes_key.lower(), bytes_value))
 
         self._encoding = encoding
diff --git a/tests/models/test_headers.py b/tests/models/test_headers.py
index a87a446784..6e6820b848 100644
--- a/tests/models/test_headers.py
+++ b/tests/models/test_headers.py
@@ -214,6 +214,12 @@ def test_parse_header_links(value, expected):
     assert all(link in all_links for link in expected)
 
 
+def test_header_encoding_error_includes_name():
+    # https://github.com/encode/httpx/issues/3400
+    with pytest.raises(UnicodeEncodeError, match="header: 'auth'"):
+        httpx.Headers({"auth": "\u0437\u0434\u0440\u0430\u0432\u0435\u0439"})
+
+
 def test_parse_header_links_no_link():
     all_links = httpx.Response(200).links
     assert all_links == {}