diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 47b359561ec..420b6c55d56 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -25,6 +25,10 @@ New Features
 
 - Added support for multidimensional initial guess and bounds in :py:meth:`DataArray.curvefit` (:issue:`7768`, :pull:`7821`).
   By `András Gunyhó <https://github.com/mgunyho>`_.
+- Add an ``errors`` option to :py:meth:`Dataset.curve_fit` that allows
+  returning NaN for the parameters and covariances of failed fits, rather than
+  failing the whole series of fits (:issue:`6317`, :pull:`7891`).
+  By `Dominik Stańczak <https://github.com/StanczakDominik>`_ and `András Gunyhó <https://github.com/mgunyho>`_.
 
 Breaking changes
 ~~~~~~~~~~~~~~~~
diff --git a/xarray/core/dataarray.py b/xarray/core/dataarray.py
index bb6a9b131ab..9635d678c36 100644
--- a/xarray/core/dataarray.py
+++ b/xarray/core/dataarray.py
@@ -6162,6 +6162,7 @@ def curvefit(
         p0: dict[str, float | DataArray] | None = None,
         bounds: dict[str, tuple[float | DataArray, float | DataArray]] | None = None,
         param_names: Sequence[str] | None = None,
+        errors: ErrorOptions = "raise",
         kwargs: dict[str, Any] | None = None,
     ) -> Dataset:
         """
@@ -6206,6 +6207,10 @@ def curvefit(
             this will be automatically determined by arguments of `func`. `param_names`
             should be manually supplied when fitting a function that takes a variable
             number of parameters.
+        errors : {"raise", "ignore"}, default: "raise"
+            If 'raise', any errors from the `scipy.optimize_curve_fit` optimization will
+            raise an exception. If 'ignore', the coefficients and covariances for the
+            coordinates where the fitting failed will be NaN.
         **kwargs : optional
             Additional keyword arguments to passed to scipy curve_fit.
 
@@ -6312,6 +6317,7 @@ def curvefit(
             p0=p0,
             bounds=bounds,
             param_names=param_names,
+            errors=errors,
             kwargs=kwargs,
         )
 
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 0f271e9d7e4..f4ba9d4f9fe 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -8631,6 +8631,7 @@ def curvefit(
         p0: dict[str, float | DataArray] | None = None,
         bounds: dict[str, tuple[float | DataArray, float | DataArray]] | None = None,
         param_names: Sequence[str] | None = None,
+        errors: ErrorOptions = "raise",
         kwargs: dict[str, Any] | None = None,
     ) -> T_Dataset:
         """
@@ -8675,6 +8676,10 @@ def curvefit(
             this will be automatically determined by arguments of `func`. `param_names`
             should be manually supplied when fitting a function that takes a variable
             number of parameters.
+        errors : {"raise", "ignore"}, default: "raise"
+            If 'raise', any errors from the `scipy.optimize_curve_fit` optimization will
+            raise an exception. If 'ignore', the coefficients and covariances for the
+            coordinates where the fitting failed will be NaN.
         **kwargs : optional
             Additional keyword arguments to passed to scipy curve_fit.
 
@@ -8757,6 +8762,9 @@ def curvefit(
                             f"dimensions {preserved_dims}."
                         )
 
+        if errors not in ["raise", "ignore"]:
+            raise ValueError('errors must be either "raise" or "ignore"')
+
         # Broadcast all coords with each other
         coords_ = broadcast(*coords_)
         coords_ = [
@@ -8793,7 +8801,15 @@ def _wrapper(Y, *args, **kwargs):
                     pcov = np.full([n_params, n_params], np.nan)
                     return popt, pcov
             x = np.squeeze(x)
-            popt, pcov = curve_fit(func, x, y, p0=p0_, bounds=(lb, ub), **kwargs)
+
+            try:
+                popt, pcov = curve_fit(func, x, y, p0=p0_, bounds=(lb, ub), **kwargs)
+            except RuntimeError:
+                if errors == "raise":
+                    raise
+                popt = np.full([n_params], np.nan)
+                pcov = np.full([n_params, n_params], np.nan)
+
             return popt, pcov
 
         result = type(self)()
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 804d1517f85..cee5afa56a4 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -4584,6 +4584,48 @@ def sine(t, a, f, p):
                 bounds={"a": (0, DataArray([1], coords={"foo": [1]}))},
             )
 
+    @requires_scipy
+    @pytest.mark.parametrize("use_dask", [True, False])
+    def test_curvefit_ignore_errors(self, use_dask: bool) -> None:
+        if use_dask and not has_dask:
+            pytest.skip("requires dask")
+
+        # nonsense function to make the optimization fail
+        def line(x, a, b):
+            if a > 10:
+                return 0
+            return a * x + b
+
+        da = DataArray(
+            [[1, 3, 5], [0, 20, 40]],
+            coords={"i": [1, 2], "x": [0.0, 1.0, 2.0]},
+        )
+
+        if use_dask:
+            da = da.chunk({"i": 1})
+
+        expected = DataArray(
+            [[2, 1], [np.nan, np.nan]], coords={"i": [1, 2], "param": ["a", "b"]}
+        )
+
+        with pytest.raises(RuntimeError, match="calls to function has reached maxfev"):
+            da.curvefit(
+                coords="x",
+                func=line,
+                # limit maximum number of calls so the optimization fails
+                kwargs=dict(maxfev=5),
+            ).compute()  # have to compute to raise the error
+
+        fit = da.curvefit(
+            coords="x",
+            func=line,
+            errors="ignore",
+            # limit maximum number of calls so the optimization fails
+            kwargs=dict(maxfev=5),
+        ).compute()
+
+        assert_allclose(fit.curvefit_coefficients, expected)
+
 
 class TestReduce:
     @pytest.fixture(autouse=True)