diff --git a/specutils/analysis/template_comparison.py b/specutils/analysis/template_comparison.py
index 42ec0b0c2..4de9fb82d 100644
--- a/specutils/analysis/template_comparison.py
+++ b/specutils/analysis/template_comparison.py
@@ -1,3 +1,5 @@
+import warnings
+
 import numpy as np
 from astropy.nddata import StdDevUncertainty
 
@@ -30,6 +32,7 @@ def _normalize_for_template_matching(observed_spectrum, template_spectrum, stdde
     """
     if stddev is None:
         stddev = observed_spectrum.uncertainty.represent_as(StdDevUncertainty).quantity
+
     num = np.nansum((observed_spectrum.flux*template_spectrum.flux) / (stddev**2))
     # We need to limit this sum to where observed_spectrum is not NaN as well.
     template_filtered = ((template_spectrum.flux / stddev)**2)
@@ -66,7 +69,8 @@ def _resample(resample_method, extrapolation_treatment):
     return None
 
 
-def _chi_square_for_templates(observed_spectrum, template_spectrum, resample_method, extrapolation_treatment):
+def _chi_square_for_templates(observed_spectrum, template_spectrum, resample_method,
+                              extrapolation_treatment, warn_no_overlap=True):
     """
     Resample the template spectrum to match the wavelength of the observed
     spectrum. Then, calculate chi2 on the flux of the two spectra.
@@ -93,11 +97,26 @@ def _chi_square_for_templates(observed_spectrum, template_spectrum, resample_met
         template_obswavelength = fluxc_resample(template_spectrum,
                                                 observed_spectrum.spectral_axis)
 
+    # With truncate, template may be smaller than observed spectrum if they don't fully overlap
+    matching_indices = np.intersect1d(observed_spectrum.spectral_axis,
+                                      template_obswavelength.spectral_axis,
+                                      return_indices=True)[1]
+    if len(matching_indices) == 0:
+        if warn_no_overlap:
+            warnings.warn("Template spectrum has no overlap with observed spectrum.")
+        return None, np.nan
+
+    observed_truncated = observed_spectrum[matching_indices.min():matching_indices.max()+1]
+
+    # If there was no overlap, we raise an error
+    #if len(template_obswavelength.flux) == 0:
+    #    raise ValueError("The template spectrum and observed spectrum have no overlap")
+
     # Convert the uncertainty to standard deviation if needed
-    stddev = observed_spectrum.uncertainty.represent_as(StdDevUncertainty).array
+    stddev = observed_truncated.uncertainty.represent_as(StdDevUncertainty).array
 
     # Normalize spectra
-    normalization = _normalize_for_template_matching(observed_spectrum,
+    normalization = _normalize_for_template_matching(observed_truncated,
                                                      template_obswavelength,
                                                      stddev)
 
@@ -262,8 +281,11 @@ def template_redshift(observed_spectrum, template_spectrum, redshift,
                                          uncertainty=template_spectrum.uncertainty,
                                          meta=template_spectrum.meta)
 
-        normalized_spectral_template, chi2 = _chi_square_for_templates(
-            observed_spectrum, redshifted_spectrum, resample_method, extrapolation_treatment)
+        normalized_spectral_template, chi2 = _chi_square_for_templates(observed_spectrum,
+                                                                       redshifted_spectrum,
+                                                                       resample_method,
+                                                                       extrapolation_treatment,
+                                                                       warn_no_overlap=False)
 
         chi2_list.append(chi2)
 
diff --git a/specutils/tests/test_template_comparison.py b/specutils/tests/test_template_comparison.py
index d7cf8978c..9132a634c 100644
--- a/specutils/tests/test_template_comparison.py
+++ b/specutils/tests/test_template_comparison.py
@@ -29,16 +29,11 @@ def test_template_match_no_overlap():
                        uncertainty=StdDevUncertainty(np.random.sample(50), unit='Jy'))
 
     # Get result from template_match
-    tm_result = template_comparison.template_match(spec, spec1)
-    assert tm_result[3] == 0.0
+    with pytest.warns(UserWarning, match="Template spectrum has no overlap with observed spectrum"):
+        tm_result = template_comparison.template_match(spec, spec1)
+    assert np.isnan(tm_result[3])
 
-    # Create new spectrum for comparison
-    spec_result = Spectrum1D(spectral_axis=spec_axis,
-                             flux=spec1.flux * template_comparison._normalize_for_template_matching(spec, spec1))
-    try:
-        assert quantity_allclose(tm_result[0].flux, spec_result.flux, atol=0.01*u.Jy)
-    except AssertionError:
-        pytest.xfail('TODO: investigate why this is failing')
+    assert tm_result[0] is None
 
 
 def test_template_match_minimal_overlap():