diff --git a/doc/changes/dev/14248.bugfix.rst b/doc/changes/dev/14248.bugfix.rst
new file mode 100644
index 00000000000..742d963823d
--- /dev/null
+++ b/doc/changes/dev/14248.bugfix.rst
@@ -0,0 +1 @@
+Fix bug where :func:`mne.io.anonymize_info` could set an incorrect date in ``info["proc_history"]``, causing an ``OverflowError`` when writing FIF files anonymized with a large ``daysback``, by `Eric Larson`_.
diff --git a/mne/_fiff/meas_info.py b/mne/_fiff/meas_info.py
index d6742531756..d402503f7f5 100644
--- a/mne/_fiff/meas_info.py
+++ b/mne/_fiff/meas_info.py
@@ -2964,8 +2964,14 @@ def _check_dates(info, prepend_error=""):
     It's needed because of the limited integer precision
     of the fix standard.
     """
-    for key in ("file_id", "meas_id"):
-        value = info.get(key)
+    to_check = [(f"[{key!r}]", info.get(key)) for key in ("file_id", "meas_id")]
+    for pi, record in enumerate(info.get("proc_history") or []):
+        prefix = f"['proc_history'][{pi}]"
+        to_check.append((f"{prefix}['block_id']", record.get("block_id")))
+        date = record.get("date")
+        if date is not None:
+            to_check.append((f"{prefix}['date']", dict(zip(("secs", "usecs"), date))))
+    for name, value in to_check:
         if value is not None:
             assert "msecs" not in value
             for key_2 in ("secs", "usecs"):
@@ -2974,7 +2980,7 @@ def _check_dates(info, prepend_error=""):
                     or value[key_2] > np.iinfo(">i4").max
                 ):
                     raise RuntimeError(
-                        f"{prepend_error}info[{key}][{key_2}] must be between "
+                        f"{prepend_error}info{name}[{key_2!r}] must be between "
                         f'"{np.iinfo(">i4").min!r}" and "{np.iinfo(">i4").max!r}", got '
                         f'"{value[key_2]!r}"'
                     )
@@ -3874,10 +3880,16 @@ def anonymize_info(info, daysback=None, keep_his=False, verbose=None):
                 record["date"] = DATE_NONE
             else:
                 this_t0 = (record["block_id"]["secs"], record["block_id"]["usecs"])
-                this_t1 = _add_timedelta_to_stamp(this_t0, -delta_t)
+                if this_t0 == DATE_NONE:
+                    this_t1 = DATE_NONE
+                else:
+                    this_t1 = _add_timedelta_to_stamp(this_t0, -delta_t)
                 record["block_id"]["secs"] = this_t1[0]
                 record["block_id"]["usecs"] = this_t1[1]
-                record["date"] = _add_timedelta_to_stamp(record["date"], -delta_t)
+                this_date = tuple(record["date"])
+                if this_date != DATE_NONE:
+                    this_date = _add_timedelta_to_stamp(this_date, -delta_t)
+                record["date"] = this_date
 
     hi = info.get("helium_info")
     if hi is not None:
diff --git a/mne/_fiff/tests/test_meas_info.py b/mne/_fiff/tests/test_meas_info.py
index 108060e2e2f..ae298be92f6 100644
--- a/mne/_fiff/tests/test_meas_info.py
+++ b/mne/_fiff/tests/test_meas_info.py
@@ -1090,10 +1090,26 @@ def test_anonymize_with_io(tmp_path, daysback):
     """Test that IO does not break anonymization and all fields."""
     raw = read_raw_fif(raw_fname).crop(0, 1)
     _complete_info(raw.info)
+    # maxwell_filter writes records whose stamps are the DATE_NONE placeholder;
+    # shifting those overflows the int32 stamp for large daysback (gh-14236)
+    raw.info["proc_history"].insert(
+        0,
+        dict(
+            block_id=_generate_meas_id(),
+            experimenter="m",
+            max_info=dict(
+                max_st=dict(), sss_ctc=dict(), sss_cal=dict(), sss_info=dict(in_order=8)
+            ),
+            date=DATE_NONE,
+        ),
+    )
     temp_path = tmp_path / "tmp_raw.fif"
     raw.save(temp_path)
     raw2 = read_raw_fif(temp_path).load_data()
     raw2.anonymize(daysback=daysback)
+    record = raw2.info["proc_history"][0]
+    assert (record["block_id"]["secs"], record["block_id"]["usecs"]) == DATE_NONE
+    assert record["date"] == DATE_NONE
     raw2.save(temp_path, overwrite=True)
     raw3 = read_raw_fif(temp_path)
     d = object_diff(raw2.info, raw3.info)