diff --git a/plutus-ledger-api/plutus-ledger-api.cabal b/plutus-ledger-api/plutus-ledger-api.cabal
index e5cf081b9a8..a7a877fe18f 100644
--- a/plutus-ledger-api/plutus-ledger-api.cabal
+++ b/plutus-ledger-api/plutus-ledger-api.cabal
@@ -131,6 +131,7 @@ library plutus-ledger-api-testlib
     PlutusLedgerApi.Test.V1.Value
     PlutusLedgerApi.Test.V2.Data.EvaluationContext
     PlutusLedgerApi.Test.V2.EvaluationContext
+    PlutusLedgerApi.Test.V2.OutputDatum
     PlutusLedgerApi.Test.V3.Data.EvaluationContext
     PlutusLedgerApi.Test.V3.EvaluationContext
 
diff --git a/plutus-ledger-api/test/Spec.hs b/plutus-ledger-api/test/Spec.hs
index 772faf953f5..1ec71bd829b 100644
--- a/plutus-ledger-api/test/Spec.hs
+++ b/plutus-ledger-api/test/Spec.hs
@@ -20,6 +20,7 @@ import Spec.Interval qualified
 import Spec.ScriptDecodeError qualified
 import Spec.V1.Data.Value qualified as Data.Value
 import Spec.V1.Value qualified as Value
+import Spec.V2.OutputDatum qualified as OutputDatum
 import Spec.Versions qualified
 
 import Test.Tasty
@@ -136,6 +137,8 @@ tests = testGroup "plutus-ledger-api"
         , Spec.CostModelParams.tests
         , Spec.ContextDecoding.tests
         , Value.test_Value
+        , Value.test_FaceValue
+        , OutputDatum.testOutputDatum
         ]
       , testGroup "Data"
         [ Spec.Data.Eval.tests
diff --git a/plutus-ledger-api/test/Spec/V1/Value.hs b/plutus-ledger-api/test/Spec/V1/Value.hs
index 422bc740752..cad7c8230cc 100644
--- a/plutus-ledger-api/test/Spec/V1/Value.hs
+++ b/plutus-ledger-api/test/Spec/V1/Value.hs
@@ -122,6 +122,11 @@ test_split = testProperty "split" . scaleTestsBy 7 $ \value ->
     let (valueL, valueR) = split value
     in Numeric.negate valueL <> valueR <=> value
 
+test_roundTripFaceValue :: TestTree
+test_roundTripFaceValue = testProperty "unFaceValue followed by FaceValue returns the original" $
+      \(faceValue :: FaceValue) ->
+      unFaceValue (FaceValue $ unFaceValue faceValue) === unFaceValue faceValue
+
 test_Value :: TestTree
 test_Value = testGroup "Value"
     [ test_laws
@@ -130,3 +135,8 @@ test_Value = testGroup "Value"
     , test_shuffle
     , test_split
     ]
+
+test_FaceValue :: TestTree
+test_FaceValue = testGroup "FaceValue"
+    [ test_roundTripFaceValue
+    ]
diff --git a/plutus-ledger-api/test/Spec/V2/OutputDatum.hs b/plutus-ledger-api/test/Spec/V2/OutputDatum.hs
new file mode 100644
index 00000000000..ac6c9717af0
--- /dev/null
+++ b/plutus-ledger-api/test/Spec/V2/OutputDatum.hs
@@ -0,0 +1,17 @@
+module Spec.V2.OutputDatum where
+
+import PlutusLedgerApi.Test.V2.OutputDatum ()
+import Test.Tasty
+import Test.Tasty.QuickCheck
+
+-- Define a test case for Arbitrary instance
+arbitraryTest :: TestTree
+arbitraryTest = testProperty "Arbitrary instance exists" $ \(_) ->
+  let _ = arbitrary :: Gen OutputDatum
+  in True
+
+-- Define the main test suite
+testOutputDatum :: TestTree
+testOutputDatum = testGroup "OutputDatum"
+  [arbitraryTest
+  ]
diff --git a/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V1/Value.hs b/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V1/Value.hs
index 90afa8a1ee4..c4e0688ffb1 100644
--- a/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V1/Value.hs
+++ b/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V1/Value.hs
@@ -69,6 +69,9 @@ instance Arbitrary FaceValue where
         , (1, FaceValue . fromIntegral <$> arbitrary @Int)
         ]
 
+instance Show FaceValue where
+    show (FaceValue value) = show value
+
 -- | A wrapper for satisfying an @Arbitrary a@ constraint without implementing an 'Arbitrary'
 -- instance for @a@.
 newtype NoArbitrary a = NoArbitrary
diff --git a/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V2/OutputDatum.hs b/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V2/OutputDatum.hs
new file mode 100644
index 00000000000..d0dc3ad1719
--- /dev/null
+++ b/plutus-ledger-api/testlib/PlutusLedgerApi/Test/V2/OutputDatum.hs
@@ -0,0 +1,28 @@
+{-# LANGUAGE LambdaCase #-}
+
+module PlutusLedgerApi.Test.V2.OutputDatum where
+
+import PlutusLedgerApi.V2
+import Test.QuickCheck
+
+instance Arbitrary OutputDatum where
+  {-# INLINEABLE arbitrary #-}
+  arbitrary =
+    oneof
+      [ pure NoOutputDatum
+      , OutputDatumHash <$> arbitrary
+      , OutputDatum <$> arbitrary
+      ]
+  {-# INLINEABLE shrink #-}
+  -- We only shrink the OutputDatum case, since the others wouldn't shrink
+  -- anyway.
+  shrink = \case
+    OutputDatum d -> OutputDatum <$> shrink d
+    _ -> []
+
+instance CoArbitrary OutputDatum where
+  {-# INLINEABLE coarbitrary #-}
+  coarbitrary = \case
+    NoOutputDatum -> variant (0 :: Int)
+    OutputDatumHash dh -> variant (1 :: Int) . coarbitrary dh
+    OutputDatum d -> variant (2 :: Int) . coarbitrary d