diff --git a/qiskit_experiments/calibration_management/calibrations.py b/qiskit_experiments/calibration_management/calibrations.py
index 3787a200ac..37ca3971ea 100644
--- a/qiskit_experiments/calibration_management/calibrations.py
+++ b/qiskit_experiments/calibration_management/calibrations.py
@@ -1063,7 +1063,13 @@ def load_parameter_values(self, file_name: str = "parameter_values.csv"):
                 param_val = ParameterValue(
                     row["value"], row["date_time"], row["valid"], row["exp_id"], row["group"]
                 )
-                key = ParameterKey(row["parameter"], self._to_tuple(row["qubits"]), row["schedule"])
+
+                if row["schedule"] == "":
+                    schedule_name = None
+                else:
+                    schedule_name = row["schedule"]
+
+                key = ParameterKey(row["parameter"], self._to_tuple(row["qubits"]), schedule_name)
                 self.add_parameter_value(param_val, *key)
 
     @classmethod
diff --git a/test/calibration/test_calibrations.py b/test/calibration/test_calibrations.py
index 161af625dd..48817ec6c0 100644
--- a/test/calibration/test_calibrations.py
+++ b/test/calibration/test_calibrations.py
@@ -31,8 +31,11 @@
 from qiskit.pulse.transforms import inline_subroutines, block_to_schedule
 import qiskit.pulse as pulse
 from qiskit.test import QiskitTestCase
+from qiskit.test.mock import FakeArmonk
 from qiskit_experiments.calibration_management.calibrations import Calibrations, ParameterKey
 from qiskit_experiments.calibration_management.parameter_value import ParameterValue
+from qiskit_experiments.calibration_management.basis_gate_library import FixedFrequencyTransmon
+from qiskit_experiments.calibration_management import BackendCalibrations
 from qiskit_experiments.exceptions import CalibrationError
 
 
@@ -1352,3 +1355,29 @@ def test_alternate_date_formats(self):
         self.addCleanup(self._remove_files, self._prefix)
         self.cals._params = defaultdict(list)
         self.cals.load_parameter_values(self._prefix + "parameter_values.csv")
+
+    def test_save_load_library(self):
+        """Test that we can load and save a library.
+
+        These libraries contain both parameters with schedules and parameters without
+        any schedules (e.g. frequencies for qubits and readout).
+        """
+
+        library = FixedFrequencyTransmon()
+        backend = FakeArmonk()
+        cals = BackendCalibrations(backend, library)
+
+        cals.parameters_table()
+
+        cals.save(file_type="csv", overwrite=True, file_prefix=self._prefix)
+
+        cals.load_parameter_values(self._prefix + "parameter_values.csv")
+
+        # Test the value of a few loaded params.
+        self.assertEqual(cals.get_parameter_value("amp", (0,), "x"), 0.5)
+        self.assertEqual(
+            cals.get_parameter_value("qubit_lo_freq", (0,)),
+            backend.defaults().qubit_freq_est[0],
+        )
+
+        self.addCleanup(self._remove_files, self._prefix)