diff --git a/pybop/costs/error_costs.py b/pybop/costs/error_costs.py
index 82582d52a..2c497d45b 100644
--- a/pybop/costs/error_costs.py
+++ b/pybop/costs/error_costs.py
@@ -10,7 +10,11 @@ class BaseCost:
 
     def __init__(self, problem):
         self.problem = problem
-        self._target = problem._target
+        if problem is not None:
+            self._target = problem._target
+            self.x0 = problem.x0
+            self.bounds = problem.bounds
+            self.n_parameters = problem.n_parameters
 
     def __call__(self, x, grad=None):
         """
@@ -18,12 +22,6 @@ def __call__(self, x, grad=None):
         """
         raise NotImplementedError
 
-    def n_parameters(self):
-        """
-        Returns the size of the parameter space.
-        """
-        raise NotImplementedError
-
 
 class RootMeanSquaredError(BaseCost):
     """
diff --git a/pybop/costs/standalone.py b/pybop/costs/standalone.py
new file mode 100644
index 000000000..197dcca5b
--- /dev/null
+++ b/pybop/costs/standalone.py
@@ -0,0 +1,18 @@
+import pybop
+import numpy as np
+
+
+class StandaloneCost(pybop.BaseCost):
+    def __init__(self, problem=None):
+        super().__init__(problem)
+
+        self.x0 = np.array([4.2])
+        self.n_parameters = len(self.x0)
+
+        self.bounds = dict(
+            lower=[-1],
+            upper=[10],
+        )
+
+    def __call__(self, x, grad=None):
+        return x[0] ** 2 + 42
diff --git a/pybop/optimisation.py b/pybop/optimisation.py
index ac8ffdfd3..6dc947de7 100644
--- a/pybop/optimisation.py
+++ b/pybop/optimisation.py
@@ -23,11 +23,11 @@ def __init__(
         verbose=False,
     ):
         self.cost = cost
-        self.problem = cost.problem
         self.optimiser = optimiser
         self.verbose = verbose
-        self.x0 = cost.problem.x0
-        self.bounds = self.problem.bounds
+        self.x0 = cost.x0
+        self.bounds = cost.bounds
+        self.n_parameters = cost.n_parameters
         self.sigma0 = sigma0
         self.log = []
 
@@ -56,7 +56,7 @@ def __init__(
             self.pints = False
 
             if issubclass(self.optimiser, pybop.NLoptOptimize):
-                self.optimiser = self.optimiser(self.problem.n_parameters)
+                self.optimiser = self.optimiser(self.n_parameters)
 
             elif issubclass(self.optimiser, pybop.SciPyMinimize):
                 self.optimiser = self.optimiser()
diff --git a/tests/unit/test_cost.py b/tests/unit/test_cost.py
index 8f528e942..0c7e329f3 100644
--- a/tests/unit/test_cost.py
+++ b/tests/unit/test_cost.py
@@ -41,8 +41,6 @@ def test_costs(self, cut_off):
         assert base_cost.problem == problem
         with pytest.raises(NotImplementedError):
             base_cost([0.5])
-        with pytest.raises(NotImplementedError):
-            base_cost.n_parameters()
 
         # Root Mean Squared Error
         rmse_cost = pybop.RootMeanSquaredError(problem)
diff --git a/tests/unit/test_optimisation.py b/tests/unit/test_optimisation.py
index b9d3b0414..406c89ee3 100644
--- a/tests/unit/test_optimisation.py
+++ b/tests/unit/test_optimisation.py
@@ -1,6 +1,7 @@
 import pybop
 import numpy as np
 import pytest
+from pybop.costs.standalone import StandaloneCost
 
 
 class TestOptimisation:
@@ -8,6 +9,20 @@ class TestOptimisation:
     A class to test the optimisation class.
     """
 
+    @pytest.mark.unit
+    def test_standalone(self):
+        # Build an Optimisation problem with a StandaloneCost
+        cost = StandaloneCost()
+
+        opt = pybop.Optimisation(cost=cost, optimiser=pybop.NLoptOptimize)
+
+        assert len(opt.x0) == opt.n_parameters
+
+        x, final_cost = opt.run()
+
+        np.testing.assert_allclose(x, 0, atol=1e-2)
+        np.testing.assert_allclose(final_cost, 42, atol=1e-2)
+
     @pytest.mark.unit
     def test_prior_sampling(self):
         # Tests prior sampling