diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 7e334219ac4c1..55e3d96ef6b88 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -505,9 +505,11 @@ Groupby/resample/rolling
 - Bug in :meth:`GroupBy.groups` with a datetime key in conjunction with another key produced incorrect number of group keys (:issue:`51158`)
 - Bug in :meth:`GroupBy.quantile` may implicitly sort the result index with ``sort=False`` (:issue:`53009`)
 - Bug in :meth:`GroupBy.var` failing to raise ``TypeError`` when called with datetime64, timedelta64 or :class:`PeriodDtype` values (:issue:`52128`, :issue:`53045`)
+- Bug in :meth:`Resampler.ohlc` with empty object returning a :class:`Series` instead of empty :class:`DataFrame` (:issue:`42902`)
 - Bug in :meth:`SeriesGroupBy.nth` and :meth:`DataFrameGroupBy.nth` after performing column selection when using ``dropna="any"`` or ``dropna="all"`` would not subset columns (:issue:`53518`)
 - Bug in :meth:`SeriesGroupBy.nth` and :meth:`DataFrameGroupBy.nth` raised after performing column selection when using ``dropna="any"`` or ``dropna="all"`` resulted in rows being dropped (:issue:`53518`)
 - Bug in :meth:`SeriesGroupBy.sum` and :meth:`DataFrameGroupby.sum` summing ``np.inf + np.inf`` and ``(-np.inf) + (-np.inf)`` to ``np.nan`` (:issue:`53606`)
+-
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index c48ad224d3645..6a4e33229690b 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -62,6 +62,7 @@
 )
 from pandas.core.groupby.grouper import Grouper
 from pandas.core.groupby.ops import BinGrouper
+from pandas.core.indexes.api import MultiIndex
 from pandas.core.indexes.datetimes import (
     DatetimeIndex,
     date_range,
@@ -1460,6 +1461,23 @@ def ohlc(
     ):
         maybe_warn_args_and_kwargs(type(self), "ohlc", args, kwargs)
         nv.validate_resampler_func("ohlc", args, kwargs)
+
+        ax = self.ax
+        obj = self._obj_with_exclusions
+        if len(ax) == 0:
+            # GH#42902
+            obj = obj.copy()
+            obj.index = _asfreq_compat(obj.index, self.freq)
+            if obj.ndim == 1:
+                obj = obj.to_frame()
+                obj = obj.reindex(["open", "high", "low", "close"], axis=1)
+            else:
+                mi = MultiIndex.from_product(
+                    [obj.columns, ["open", "high", "low", "close"]]
+                )
+                obj = obj.reindex(mi, axis=1)
+            return obj
+
         return self._downsample("ohlc")
 
     @doc(SeriesGroupBy.nunique)
diff --git a/pandas/tests/resample/test_base.py b/pandas/tests/resample/test_base.py
index e57d938f060df..22bd8f9c8ced3 100644
--- a/pandas/tests/resample/test_base.py
+++ b/pandas/tests/resample/test_base.py
@@ -5,6 +5,7 @@
 
 from pandas import (
     DataFrame,
+    MultiIndex,
     NaT,
     PeriodIndex,
     Series,
@@ -100,16 +101,9 @@ def test_raises_on_non_datetimelike_index():
 
 @all_ts
 @pytest.mark.parametrize("freq", ["M", "D", "H"])
-def test_resample_empty_series(freq, empty_series_dti, resample_method, request):
+def test_resample_empty_series(freq, empty_series_dti, resample_method):
     # GH12771 & GH12868
 
-    if resample_method == "ohlc" and isinstance(empty_series_dti.index, PeriodIndex):
-        request.node.add_marker(
-            pytest.mark.xfail(
-                reason=f"GH13083: {resample_method} fails for PeriodIndex"
-            )
-        )
-
     ser = empty_series_dti
     if freq == "M" and isinstance(ser.index, TimedeltaIndex):
         msg = (
@@ -123,12 +117,19 @@ def test_resample_empty_series(freq, empty_series_dti, resample_method, request)
     rs = ser.resample(freq)
     result = getattr(rs, resample_method)()
 
-    expected = ser.copy()
-    expected.index = _asfreq_compat(ser.index, freq)
+    if resample_method == "ohlc":
+        expected = DataFrame(
+            [], index=ser.index[:0].copy(), columns=["open", "high", "low", "close"]
+        )
+        expected.index = _asfreq_compat(ser.index, freq)
+        tm.assert_frame_equal(result, expected, check_dtype=False)
+    else:
+        expected = ser.copy()
+        expected.index = _asfreq_compat(ser.index, freq)
+        tm.assert_series_equal(result, expected, check_dtype=False)
 
     tm.assert_index_equal(result.index, expected.index)
     assert result.index.freq == expected.index.freq
-    tm.assert_series_equal(result, expected, check_dtype=False)
 
 
 @all_ts
@@ -203,7 +204,15 @@ def test_resample_empty_dataframe(empty_frame_dti, freq, resample_method):
 
     rs = df.resample(freq, group_keys=False)
     result = getattr(rs, resample_method)()
-    if resample_method != "size":
+    if resample_method == "ohlc":
+        # TODO: no tests with len(df.columns) > 0
+        mi = MultiIndex.from_product([df.columns, ["open", "high", "low", "close"]])
+        expected = DataFrame(
+            [], index=df.index[:0].copy(), columns=mi, dtype=np.float64
+        )
+        expected.index = _asfreq_compat(df.index, freq)
+
+    elif resample_method != "size":
         expected = df.copy()
     else:
         # GH14962