diff --git a/test/optimisation/Optimisation.jl b/test/optimisation/Optimisation.jl
index 498852231..d8afd83db 100644
--- a/test/optimisation/Optimisation.jl
+++ b/test/optimisation/Optimisation.jl
@@ -619,14 +619,28 @@ using Turing
         @assert get(result, :c) == (; :c => Array{Float64}[])
     end
 
-    @testset "ADType" for adbackend in ADUtils.adbackends
+    @testset "ADType test with $adbackend" for adbackend in ADUtils.adbackends
         Random.seed!(222)
         m = DynamicPPL.contextualize(
             gdemo_default, ADUtils.ADTypeCheckContext(adbackend, gdemo_default.context)
         )
-        # These will error if the adbackend being used is not the one set.
-        maximum_likelihood(m; adtype=adbackend)
-        maximum_a_posteriori(m; adtype=adbackend)
+        if adbackend isa AutoMooncake
+            # Optimization.jl does not support Mooncake as an AD backend, see
+            # https://docs.sciml.ai/Optimization/stable/API/ad/#ad
+            # If it ever does, then we should just run them to make sure they don't error
+            err_msg = "The passed automatic differentiation backend choice is not available"
+            @test_throws err_msg maximum_likelihood(m; adtype=adbackend)
+            @test_throws err_msg maximum_a_posteriori(m; adtype=adbackend)
+        elseif adbackend isa AutoForwardDiff
+            # TODO: Figure out why this is happening.
+            # https://github.com/TuringLang/Turing.jl/issues/2369
+            @test_throws DivideError maximum_likelihood(m; adtype=adbackend)
+            @test_throws DivideError maximum_a_posteriori(m; adtype=adbackend)
+        else
+            # These will error if the adbackend being used is not the one set.
+            maximum_likelihood(m; adtype=adbackend)
+            maximum_a_posteriori(m; adtype=adbackend)
+        end
     end
 end