diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 9db30ce710c0d..dcc28446f50e5 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -657,7 +657,7 @@ def get_value(self, series, key):
             return series.take(locs)
 
         try:
-            return com.maybe_box(self, Index.get_value(self, series, key), series, key)
+            value = Index.get_value(self, series, key)
         except KeyError:
             try:
                 loc = self._get_string_slice(key)
@@ -669,6 +669,8 @@ def get_value(self, series, key):
                 return self.get_value_maybe_box(series, key)
             except (TypeError, ValueError, KeyError):
                 raise KeyError(key)
+        else:
+            return com.maybe_box(self, value, series, key)
 
     def get_value_maybe_box(self, series, key):
         # needed to localize naive datetimes
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index d34ac1a541d27..5815d4a8ecb16 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -509,7 +509,7 @@ def get_value(self, series, key):
         """
         s = com.values_from_object(series)
         try:
-            return com.maybe_box(self, super().get_value(s, key), series, key)
+            value = super().get_value(s, key)
         except (KeyError, IndexError):
             if isinstance(key, str):
                 asdt, parsed, reso = parse_time_string(key, self.freq)
@@ -541,6 +541,8 @@ def get_value(self, series, key):
             period = Period(key, self.freq)
             key = period.value if isna(period) else period.ordinal
             return com.maybe_box(self, self._int64index.get_value(s, key), series, key)
+        else:
+            return com.maybe_box(self, value, series, key)
 
     @Appender(_index_shared_docs["get_indexer"] % _index_doc_kwargs)
     def get_indexer(self, target, method=None, limit=None, tolerance=None):