diff --git a/openmc/executor.py b/openmc/executor.py
index 76d100d32a..ebd1a450bc 100644
--- a/openmc/executor.py
+++ b/openmc/executor.py
@@ -11,10 +11,6 @@ def _run(args, output, cwd):
     p = subprocess.Popen(args, cwd=cwd, stdout=subprocess.PIPE,
                          stderr=subprocess.STDOUT, universal_newlines=True)
 
-    # Compile a regex object to identify statepoint writes
-    sp_rxprog = re.compile(r'Creating state point (.+)\.\.\.')
-    last_statepoint = None
-
     # Capture and re-print OpenMC output in real-time
     lines = []
     while True:
@@ -23,11 +19,6 @@ def _run(args, output, cwd):
         if not line and p.poll() is not None:
             break
 
-        # If a statepoint was written, capture its filename
-        sp_match = sp_rxprog.search(line)
-        if sp_match:
-            last_statepoint = sp_match.group(1)
-
         lines.append(line)
         if output:
             # If user requested output, print to screen
@@ -37,7 +28,6 @@ def _run(args, output, cwd):
     if p.returncode != 0:
         raise subprocess.CalledProcessError(p.returncode, ' '.join(args),
                                             ''.join(lines))
-    return last_statepoint
 
 
 def plot_geometry(output=True, openmc_exec='openmc', cwd='.'):
@@ -195,11 +185,6 @@ def run(particles=None, threads=None, geometry_debug=False,
     event_based : bool, optional
         Turns on event-based parallelism, instead of default history-based
 
-    Returns
-    -------
-    str
-        Name of the last written statepoint file, or None
-
     Raises
     ------
     subprocess.CalledProcessError
@@ -229,4 +214,4 @@ def run(particles=None, threads=None, geometry_debug=False,
     if mpi_args is not None:
         args = mpi_args + args
 
-    return _run(args, output, cwd)
+    _run(args, output, cwd)
diff --git a/openmc/model/model.py b/openmc/model/model.py
index e59c679b52..2089721032 100644
--- a/openmc/model/model.py
+++ b/openmc/model/model.py
@@ -1,5 +1,6 @@
 from collections.abc import Iterable
 from pathlib import Path
+import time
 
 import openmc
 from openmc.checkvalue import check_type, check_value
@@ -175,7 +176,7 @@ class Model:
             will be created.
 
         """
-        # Create directory if
+        # Create directory if required
         d = Path(directory)
         if not d.is_dir():
             d.mkdir(parents=True)
@@ -201,7 +202,7 @@ class Model:
 
     def run(self, **kwargs):
         """Creates the XML files, runs OpenMC, and returns k-effective.
-        The last statepoint filename is available in model.statepoint
+        The last statepoint Path is available in model.statepoint
 
         Parameters
         ----------
@@ -211,14 +212,32 @@ class Model:
         Returns
         -------
         uncertainties.UFloat
-            Combined estimator of k-effective from the statepoint
+            Combined estimator of k-effective from the last statepoint
+            (None if no statepoint was written)
 
         """
 
         self.export_to_xml()
 
-        self.statepoint = openmc.run(**kwargs)
+        # Setting tstart here ensures we don't pick up any old statepoint
+        # files that might preexist in the output directory
+        tstart = time.time()
+        self.statepoint = None
 
+        openmc.run(**kwargs)
+
+        # Get output directory and last statepoint written by this run
+        if self.settings.output and 'path' in self.settings.output:
+            output_dir = Path(self.settings.output['path'])
+        else:
+            output_dir = Path.cwd()
+        for sp in output_dir.glob('statepoint.*.h5'):
+            mtime = sp.stat().st_mtime
+            if mtime >= tstart:  # >= allows for poor clock resolution
+                tstart = mtime
+                self.statepoint = sp
+
+        # Open the last statepoint to get the final k-effective
         keff = None
         if self.statepoint:
             with openmc.StatePoint(self.statepoint) as sp:
diff --git a/tests/regression_tests/trigger_statepoint_restart/inputs_true.dat b/tests/regression_tests/trigger_statepoint_restart/inputs_true.dat
index decc87b0c5..26890f9f86 100644
--- a/tests/regression_tests/trigger_statepoint_restart/inputs_true.dat
+++ b/tests/regression_tests/trigger_statepoint_restart/inputs_true.dat
@@ -25,6 +25,7 @@
     <max_batches>1000</max_batches>
     <batch_interval>1</batch_interval>
   </trigger>
+  <verbosity>1</verbosity>
 </settings>
 <?xml version='1.0' encoding='utf-8'?>
 <tallies>
diff --git a/tests/regression_tests/trigger_statepoint_restart/test.py b/tests/regression_tests/trigger_statepoint_restart/test.py
index 961a576a55..44b809454b 100644
--- a/tests/regression_tests/trigger_statepoint_restart/test.py
+++ b/tests/regression_tests/trigger_statepoint_restart/test.py
@@ -33,6 +33,7 @@ def model():
     settings.trigger_max_batches = 1000
     settings.trigger_batch_interval = 1
     settings.trigger_active = True
+    settings.verbosity = 1 # to test that this works even with no output
  
     # Tallies
     tallies = openmc.Tallies()
@@ -88,6 +89,7 @@ class TriggerStatepointRestartTestHarness(PyAPITestHarness):
             # First non-restart run
             k_combined_1 = self._model.run(**args)
             sp_batchno_1 = 0
+            assert self._model.statepoint
             with openmc.StatePoint(self._model.statepoint) as sp:
                  sp_batchno_1 = sp.current_batch
             assert sp_batchno_1 > 10
@@ -102,6 +104,7 @@ class TriggerStatepointRestartTestHarness(PyAPITestHarness):
             args['restart_file'] = restart_spfile[0]
             k_combined_2 = self._model.run(**args)
             sp_batchno_2 = 0
+            assert self._model.statepoint
             with openmc.StatePoint(self._model.statepoint) as sp:
                  sp_batchno_2 = sp.current_batch
             assert sp_batchno_2 > 10