diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index b804ed883e693..7f7dd62540387 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -3598,9 +3598,10 @@ cpdef to_offset(freq):
                 if not stride:
                     stride = 1
 
-                from .resolution import Resolution  # TODO: avoid runtime import
+                # TODO: avoid runtime import
+                from .resolution import Resolution, reso_str_bump_map
 
-                if prefix in Resolution.reso_str_bump_map:
+                if prefix in reso_str_bump_map:
                     stride, name = Resolution.get_stride_from_decimal(
                         float(stride), prefix
                     )
diff --git a/pandas/_libs/tslibs/resolution.pyx b/pandas/_libs/tslibs/resolution.pyx
index 2133573ee7554..b3fc1e32f68e8 100644
--- a/pandas/_libs/tslibs/resolution.pyx
+++ b/pandas/_libs/tslibs/resolution.pyx
@@ -1,3 +1,5 @@
+from enum import Enum
+
 import numpy as np
 from numpy cimport ndarray, int64_t, int32_t
 
@@ -25,10 +27,46 @@ cdef:
     int RESO_HR = 5
     int RESO_DAY = 6
 
+reso_str_bump_map = {
+    "D": "H",
+    "H": "T",
+    "T": "S",
+    "S": "L",
+    "L": "U",
+    "U": "N",
+    "N": None,
+}
+
+_abbrev_to_attrnames = {v: k for k, v in attrname_to_abbrevs.items()}
+
+_reso_str_map = {
+    RESO_NS: "nanosecond",
+    RESO_US: "microsecond",
+    RESO_MS: "millisecond",
+    RESO_SEC: "second",
+    RESO_MIN: "minute",
+    RESO_HR: "hour",
+    RESO_DAY: "day",
+}
+
+_str_reso_map = {v: k for k, v in _reso_str_map.items()}
+
+# factor to multiply a value by to convert it to the next finer grained
+# resolution
+_reso_mult_map = {
+    RESO_NS: None,
+    RESO_US: 1000,
+    RESO_MS: 1000,
+    RESO_SEC: 1000,
+    RESO_MIN: 60,
+    RESO_HR: 60,
+    RESO_DAY: 24,
+}
 
 # ----------------------------------------------------------------------
 
-def resolution(const int64_t[:] stamps, tz=None):
+
+def get_resolution(const int64_t[:] stamps, tz=None):
     cdef:
         Py_ssize_t i, n = len(stamps)
         npy_datetimestruct dts
@@ -82,7 +120,7 @@ def resolution(const int64_t[:] stamps, tz=None):
                 if curr_reso < reso:
                     reso = curr_reso
 
-    return reso
+    return Resolution(reso)
 
 
 cdef inline int _reso_stamp(npy_datetimestruct *dts):
@@ -99,7 +137,7 @@ cdef inline int _reso_stamp(npy_datetimestruct *dts):
     return RESO_DAY
 
 
-class Resolution:
+class Resolution(Enum):
 
     # Note: cython won't allow us to reference the cdef versions at the
     # module level
@@ -111,41 +149,14 @@ class Resolution:
     RESO_HR = 5
     RESO_DAY = 6
 
-    _reso_str_map = {
-        RESO_NS: 'nanosecond',
-        RESO_US: 'microsecond',
-        RESO_MS: 'millisecond',
-        RESO_SEC: 'second',
-        RESO_MIN: 'minute',
-        RESO_HR: 'hour',
-        RESO_DAY: 'day'}
-
-    # factor to multiply a value by to convert it to the next finer grained
-    # resolution
-    _reso_mult_map = {
-        RESO_NS: None,
-        RESO_US: 1000,
-        RESO_MS: 1000,
-        RESO_SEC: 1000,
-        RESO_MIN: 60,
-        RESO_HR: 60,
-        RESO_DAY: 24}
-
-    reso_str_bump_map = {
-        'D': 'H',
-        'H': 'T',
-        'T': 'S',
-        'S': 'L',
-        'L': 'U',
-        'U': 'N',
-        'N': None}
-
-    _str_reso_map = {v: k for k, v in _reso_str_map.items()}
-
-    _freq_reso_map = {v: k for k, v in attrname_to_abbrevs.items()}
+    def __lt__(self, other):
+        return self.value < other.value
+
+    def __ge__(self, other):
+        return self.value >= other.value
 
     @classmethod
-    def get_str(cls, reso: int) -> str:
+    def get_str(cls, reso: "Resolution") -> str:
         """
         Return resolution str against resolution code.
 
@@ -154,10 +165,10 @@ class Resolution:
         >>> Resolution.get_str(Resolution.RESO_SEC)
         'second'
         """
-        return cls._reso_str_map.get(reso, 'day')
+        return _reso_str_map[reso.value]
 
     @classmethod
-    def get_reso(cls, resostr: str) -> int:
+    def get_reso(cls, resostr: str) -> "Resolution":
         """
         Return resolution str against resolution code.
 
@@ -169,25 +180,27 @@ class Resolution:
         >>> Resolution.get_reso('second') == Resolution.RESO_SEC
         True
         """
-        return cls._str_reso_map.get(resostr, cls.RESO_DAY)
+        return cls(_str_reso_map[resostr])
 
     @classmethod
-    def get_str_from_freq(cls, freq: str) -> str:
+    def get_attrname_from_abbrev(cls, freq: str) -> str:
         """
         Return resolution str against frequency str.
 
         Examples
         --------
-        >>> Resolution.get_str_from_freq('H')
+        >>> Resolution.get_attrname_from_abbrev('H')
         'hour'
         """
-        return cls._freq_reso_map.get(freq, 'day')
+        return _abbrev_to_attrnames[freq]
 
     @classmethod
-    def get_reso_from_freq(cls, freq: str) -> int:
+    def get_reso_from_freq(cls, freq: str) -> "Resolution":
         """
         Return resolution code against frequency str.
 
+        `freq` is given by the `offset.freqstr` for some DateOffset object.
+
         Examples
         --------
         >>> Resolution.get_reso_from_freq('H')
@@ -196,16 +209,16 @@ class Resolution:
         >>> Resolution.get_reso_from_freq('H') == Resolution.RESO_HR
         True
         """
-        return cls.get_reso(cls.get_str_from_freq(freq))
+        return cls.get_reso(cls.get_attrname_from_abbrev(freq))
 
     @classmethod
-    def get_stride_from_decimal(cls, value, freq):
+    def get_stride_from_decimal(cls, value: float, freq: str):
         """
         Convert freq with decimal stride into a higher freq with integer stride
 
         Parameters
         ----------
-        value : int or float
+        value : float
         freq : str
             Frequency string
 
@@ -229,13 +242,13 @@ class Resolution:
             return int(value), freq
         else:
             start_reso = cls.get_reso_from_freq(freq)
-            if start_reso == 0:
+            if start_reso.value == 0:
                 raise ValueError(
                     "Could not convert to integer offset at any resolution"
                 )
 
-            next_value = cls._reso_mult_map[start_reso] * value
-            next_name = cls.reso_str_bump_map[freq]
+            next_value = _reso_mult_map[start_reso.value] * value
+            next_name = reso_str_bump_map[freq]
             return cls.get_stride_from_decimal(next_value, next_name)
 
 
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index cf3cde155a3bb..b9f712e4d64fe 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1,6 +1,6 @@
 from datetime import datetime, timedelta
 import operator
-from typing import Any, Callable, Sequence, Tuple, Type, TypeVar, Union, cast
+from typing import Any, Callable, Optional, Sequence, Tuple, Type, TypeVar, Union, cast
 import warnings
 
 import numpy as np
@@ -804,7 +804,7 @@ def _validate_scalar(self, value, msg: str, cast_str: bool = False):
         return value
 
     def _validate_listlike(
-        self, value, opname: str, cast_str: bool = False, allow_object: bool = False,
+        self, value, opname: str, cast_str: bool = False, allow_object: bool = False
     ):
         if isinstance(value, type(self)):
             return value
@@ -1103,14 +1103,22 @@ def inferred_freq(self):
             return None
 
     @property  # NB: override with cache_readonly in immutable subclasses
-    def _resolution(self):
-        return Resolution.get_reso_from_freq(self.freqstr)
+    def _resolution(self) -> Optional[Resolution]:
+        try:
+            return Resolution.get_reso_from_freq(self.freqstr)
+        except KeyError:
+            return None
 
     @property  # NB: override with cache_readonly in immutable subclasses
     def resolution(self) -> str:
         """
         Returns day, hour, minute, second, millisecond or microsecond
         """
+        if self._resolution is None:
+            if is_period_dtype(self.dtype):
+                # somewhere in the past it was decided we default to day
+                return "day"
+            # otherwise we fall through and will raise
         return Resolution.get_str(self._resolution)
 
     @classmethod
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 894a519cb693e..4e31477571a5f 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -538,8 +538,8 @@ def is_normalized(self):
         return conversion.is_date_array_normalized(self.asi8, self.tz)
 
     @property  # NB: override with cache_readonly in immutable subclasses
-    def _resolution(self):
-        return libresolution.resolution(self.asi8, self.tz)
+    def _resolution(self) -> libresolution.Resolution:
+        return libresolution.get_resolution(self.asi8, self.tz)
 
     # ----------------------------------------------------------------
     # Array-Like / EA-Interface Methods
diff --git a/pandas/tests/tseries/frequencies/test_freq_code.py b/pandas/tests/tseries/frequencies/test_freq_code.py
index 1c51ad0c45238..51554854378ea 100644
--- a/pandas/tests/tseries/frequencies/test_freq_code.py
+++ b/pandas/tests/tseries/frequencies/test_freq_code.py
@@ -104,13 +104,13 @@ def test_get_to_timestamp_base(freqstr, exp_freqstr):
         ("N", "nanosecond"),
     ],
 )
-def test_get_str_from_freq(freqstr, expected):
-    assert _reso.get_str_from_freq(freqstr) == expected
+def test_get_attrname_from_abbrev(freqstr, expected):
+    assert _reso.get_attrname_from_abbrev(freqstr) == expected
 
 
 @pytest.mark.parametrize("freq", ["A", "Q", "M", "D", "H", "T", "S", "L", "U", "N"])
 def test_get_freq_roundtrip(freq):
-    result = _attrname_to_abbrevs[_reso.get_str_from_freq(freq)]
+    result = _attrname_to_abbrevs[_reso.get_attrname_from_abbrev(freq)]
     assert freq == result