diff --git a/pandas/_libs/tslibs/tzconversion.pxd b/pandas/_libs/tslibs/tzconversion.pxd
index 1990afd77a8fb..3666d00707ac8 100644
--- a/pandas/_libs/tslibs/tzconversion.pxd
+++ b/pandas/_libs/tslibs/tzconversion.pxd
@@ -2,7 +2,9 @@ from cpython.datetime cimport tzinfo
 from numpy cimport int64_t
 
 
-cdef int64_t tz_convert_utc_to_tzlocal(int64_t utc_val, tzinfo tz, bint* fold=*)
+cdef int64_t tz_convert_utc_to_tzlocal(
+    int64_t utc_val, tzinfo tz, bint* fold=*
+) except? -1
 cpdef int64_t tz_convert_from_utc_single(int64_t val, tzinfo tz)
 cdef int64_t tz_localize_to_utc_single(
     int64_t val, tzinfo tz, object ambiguous=*, object nonexistent=*
diff --git a/pandas/_libs/tslibs/tzconversion.pyx b/pandas/_libs/tslibs/tzconversion.pyx
index 4a3fac1954ab7..f08a86b1262e6 100644
--- a/pandas/_libs/tslibs/tzconversion.pyx
+++ b/pandas/_libs/tslibs/tzconversion.pyx
@@ -355,7 +355,9 @@ cdef inline str _render_tstamp(int64_t val):
 # ----------------------------------------------------------------------
 # Timezone Conversion
 
-cdef int64_t tz_convert_utc_to_tzlocal(int64_t utc_val, tzinfo tz, bint* fold=NULL):
+cdef int64_t tz_convert_utc_to_tzlocal(
+    int64_t utc_val, tzinfo tz, bint* fold=NULL
+) except? -1:
     """
     Parameters
     ----------
@@ -549,8 +551,10 @@ cdef inline int64_t _tzlocal_get_offset_components(int64_t val, tzinfo tz,
     return int(td.total_seconds() * 1_000_000_000)
 
 
+# OSError may be thrown by tzlocal on windows at or close to 1970-01-01
+#  see https://github.com/pandas-dev/pandas/pull/37591#issuecomment-720628241
 cdef int64_t _tz_convert_tzlocal_utc(int64_t val, tzinfo tz, bint to_utc=True,
-                                     bint* fold=NULL):
+                                     bint* fold=NULL) except? -1:
     """
     Convert the i8 representation of a datetime from a tzlocal timezone to
     UTC, or vice-versa.
diff --git a/pandas/tests/frame/test_reductions.py b/pandas/tests/frame/test_reductions.py
index fbb51b70d34fd..374d185f45844 100644
--- a/pandas/tests/frame/test_reductions.py
+++ b/pandas/tests/frame/test_reductions.py
@@ -1,9 +1,11 @@
 from datetime import timedelta
 from decimal import Decimal
 
+from dateutil.tz import tzlocal
 import numpy as np
 import pytest
 
+from pandas.compat import is_platform_windows
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -1172,6 +1174,12 @@ def test_min_max_dt64_with_NaT(self):
     def test_min_max_dt64_with_NaT_skipna_false(self, tz_naive_fixture):
         # GH#36907
         tz = tz_naive_fixture
+        if isinstance(tz, tzlocal) and is_platform_windows():
+            pytest.xfail(
+                reason="GH#37659 OSError raised within tzlocal bc Windows "
+                "chokes in times before 1970-01-01"
+            )
+
         df = DataFrame(
             {
                 "a": [
diff --git a/pandas/tests/indexes/datetimes/test_ops.py b/pandas/tests/indexes/datetimes/test_ops.py
index 1d64fde103e9e..0359ee17f87c5 100644
--- a/pandas/tests/indexes/datetimes/test_ops.py
+++ b/pandas/tests/indexes/datetimes/test_ops.py
@@ -1,8 +1,11 @@
 from datetime import datetime
 
+from dateutil.tz import tzlocal
 import numpy as np
 import pytest
 
+from pandas.compat import IS64
+
 import pandas as pd
 from pandas import (
     DateOffset,
@@ -106,24 +109,27 @@ def test_repeat(self, tz_naive_fixture):
         with pytest.raises(ValueError, match=msg):
             np.repeat(rng, reps, axis=1)
 
-    def test_resolution(self, tz_naive_fixture):
+    @pytest.mark.parametrize(
+        "freq,expected",
+        [
+            ("A", "day"),
+            ("Q", "day"),
+            ("M", "day"),
+            ("D", "day"),
+            ("H", "hour"),
+            ("T", "minute"),
+            ("S", "second"),
+            ("L", "millisecond"),
+            ("U", "microsecond"),
+        ],
+    )
+    def test_resolution(self, tz_naive_fixture, freq, expected):
         tz = tz_naive_fixture
-        for freq, expected in zip(
-            ["A", "Q", "M", "D", "H", "T", "S", "L", "U"],
-            [
-                "day",
-                "day",
-                "day",
-                "day",
-                "hour",
-                "minute",
-                "second",
-                "millisecond",
-                "microsecond",
-            ],
-        ):
-            idx = pd.date_range(start="2013-04-01", periods=30, freq=freq, tz=tz)
-            assert idx.resolution == expected
+        if freq == "A" and not IS64 and isinstance(tz, tzlocal):
+            pytest.xfail(reason="OverflowError inside tzlocal past 2038")
+
+        idx = pd.date_range(start="2013-04-01", periods=30, freq=freq, tz=tz)
+        assert idx.resolution == expected
 
     def test_value_counts_unique(self, tz_naive_fixture):
         tz = tz_naive_fixture
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index fba123e47feb2..fca1316493e85 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -1,6 +1,7 @@
 from datetime import date, datetime, time as dt_time, timedelta
 from typing import Dict, List, Optional, Tuple, Type
 
+from dateutil.tz import tzlocal
 import numpy as np
 import pytest
 
@@ -14,6 +15,7 @@
 import pandas._libs.tslibs.offsets as liboffsets
 from pandas._libs.tslibs.offsets import ApplyTypeError, _get_offset, _offset_map
 from pandas._libs.tslibs.period import INVALID_FREQ_ERR_MSG
+from pandas.compat import IS64
 from pandas.compat.numpy import np_datetime64_compat
 from pandas.errors import PerformanceWarning
 
@@ -129,6 +131,8 @@ def test_apply_out_of_range(self, tz_naive_fixture):
         tz = tz_naive_fixture
         if self._offset is None:
             return
+        if isinstance(tz, tzlocal) and not IS64:
+            pytest.xfail(reason="OverflowError inside tzlocal past 2038")
 
         # try to create an out-of-bounds result timestamp; if we can't create
         # the offset skip