diff --git a/src/humanize/time.py b/src/humanize/time.py
index 4a07d52..4b0fec2 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -313,7 +313,36 @@ def _convert_aware_datetime(
     return value
 
 
-def naturalday(value: dt.date | dt.datetime, format: str = "%b %d") -> str:
+def _reference_date(
+    value: dt.date | dt.datetime,
+    when: dt.date | dt.datetime | None,
+) -> dt.date:
+    """Return the calendar date used to compare a date-like value."""
+    import datetime as dt
+
+    if when is None:
+        if isinstance(value, dt.datetime) and value.tzinfo is not None:
+            return dt.datetime.now(value.tzinfo).date()
+        return dt.date.today()
+    if isinstance(when, dt.datetime):
+        if (
+            isinstance(value, dt.datetime)
+            and value.tzinfo is not None
+            and when.tzinfo is not None
+        ):
+            when = when.astimezone(value.tzinfo)
+        return when.date()
+    if isinstance(when, dt.date):
+        return when
+    raise TypeError("when must be a date, datetime, or None")
+
+
+def naturalday(
+    value: dt.date | dt.datetime,
+    format: str = "%b %d",
+    *,
+    when: dt.date | dt.datetime | None = None,
+) -> str:
     """Return a natural day.
 
     For date values that are tomorrow, today or yesterday compared to
@@ -324,12 +353,7 @@ def naturalday(value: dt.date | dt.datetime, format: str = "%b %d") -> str:
     import datetime as dt
 
     try:
-        # When value is a tz-aware datetime, compute "today" in that timezone
-        # so the comparison uses the correct local date.
-        if isinstance(value, dt.datetime) and value.tzinfo is not None:
-            today = dt.datetime.now(value.tzinfo).date()
-        else:
-            today = dt.date.today()
+        today = _reference_date(value, when)
         value = dt.date(value.year, value.month, value.day)
     except AttributeError:
         # Passed value wasn't date-ish
@@ -351,16 +375,17 @@ def naturalday(value: dt.date | dt.datetime, format: str = "%b %d") -> str:
     return value.strftime(format)
 
 
-def naturaldate(value: dt.date | dt.datetime) -> str:
+def naturaldate(
+    value: dt.date | dt.datetime,
+    *,
+    when: dt.date | dt.datetime | None = None,
+) -> str:
     """Like `naturalday`, but append a year for dates more than ~five months away."""
     import datetime as dt
 
     original_value = value
     try:
-        if isinstance(value, dt.datetime) and value.tzinfo is not None:
-            today = dt.datetime.now(value.tzinfo).date()
-        else:
-            today = dt.date.today()
+        today = _reference_date(value, when)
         value = dt.date(value.year, value.month, value.day)
     except AttributeError:
         # Passed value wasn't date-ish
@@ -370,8 +395,8 @@ def naturaldate(value: dt.date | dt.datetime) -> str:
         return str(value)
     delta = _abs_timedelta(value - today)
     if delta.days >= 5 * 365 / 12:
-        return naturalday(original_value, "%b %d %Y")
-    return naturalday(original_value)
+        return naturalday(original_value, "%b %d %Y", when=when)
+    return naturalday(original_value, when=when)
 
 
 def _quotient_and_remainder(