diff --git a/cardano-api/src/Cardano/Api/Experimental/Tx/Internal/Fee.hs b/cardano-api/src/Cardano/Api/Experimental/Tx/Internal/Fee.hs
index 7ce8ebf6d5..4aa90b05cd 100644
--- a/cardano-api/src/Cardano/Api/Experimental/Tx/Internal/Fee.hs
+++ b/cardano-api/src/Cardano/Api/Experimental/Tx/Internal/Fee.hs
@@ -25,6 +25,7 @@ module Cardano.Api.Experimental.Tx.Internal.Fee
   , indexWitnessedTxProposalProcedures
   , makeTransactionBodyAutoBalance
   -- Internal
+  , calcMinFeeRecursiveWith
   , toUnsigned
   )
 where
@@ -754,7 +755,38 @@ calcMinFeeRecursive
   -> Int
   -- ^ Number of extra key hashes for native scripts
   -> Either FeeCalculationError (UnsignedTx (LedgerEra era))
-calcMinFeeRecursive changeAddr unsignedTx utxo pparams poolids stakeDelegDeposits drepDelegDeposits nExtraWitnesses
+calcMinFeeRecursive = calcMinFeeRecursiveWith 50
+
+-- | Like 'calcMinFeeRecursive' but with a configurable maximum iteration
+-- limit. Exported for testing purposes to exercise the
+-- 'FeeCalculationDidNotConverge' error path by passing a small limit.
+calcMinFeeRecursiveWith
+  :: forall era
+   . IsEra era
+  => Int
+  -- ^ Maximum number of iterations before returning
+  -- 'FeeCalculationDidNotConverge'. 'calcMinFeeRecursive' uses 50.
+  -> L.Addr
+  -- ^ Change address. Any surplus value (ADA and/or native tokens) is
+  -- sent to a new output at this address, appended at the end of the
+  -- existing outputs.
+  -> UnsignedTx (LedgerEra era)
+  -> L.UTxO (LedgerEra era)
+  -> L.PParams (LedgerEra era)
+  -> Set PoolId
+  -- ^ The set of registered stake pools. Pool registrations for pools
+  -- already in this set are treated as re-registrations (no deposit
+  -- required on the produced side).
+  -> Map StakeCredential L.Coin
+  -- ^ Deposits for stake credentials being deregistered in this
+  -- transaction. These are counted as refunds on the consumed side.
+  -> Map (Ledger.Credential Ledger.DRepRole) L.Coin
+  -- ^ Deposits for DRep credentials being deregistered in this
+  -- transaction. These are counted as refunds on the consumed side.
+  -> Int
+  -- ^ Number of extra key hashes for native scripts
+  -> Either FeeCalculationError (UnsignedTx (LedgerEra era))
+calcMinFeeRecursiveWith maxIterations changeAddr unsignedTx utxo pparams poolids stakeDelegDeposits drepDelegDeposits nExtraWitnesses
   -- If multi-assets are non-negative initially, they stay non-negative across
   -- iterations (only ADA and fee change), so check once upfront.
   | multiAssetIsNegative =
@@ -777,8 +809,6 @@ calcMinFeeRecursive changeAddr unsignedTx utxo pparams poolids stakeDelegDeposit
   multiAssetIsNegative =
     obtainCommonConstraints (useEra @era) $
       not (L.pointwise (>=) (L.MaryValue (L.Coin 0) multiAssets) mempty)
-  maxIterations :: Int
-  maxIterations = 50
 
   go
     :: Int
diff --git a/cardano-api/test/cardano-api-test/Test/Cardano/Api/Experimental.hs b/cardano-api/test/cardano-api-test/Test/Cardano/Api/Experimental.hs
index e69f5058fb..85210da312 100644
--- a/cardano-api/test/cardano-api-test/Test/Cardano/Api/Experimental.hs
+++ b/cardano-api/test/cardano-api-test/Test/Cardano/Api/Experimental.hs
@@ -14,6 +14,7 @@ import Cardano.Api qualified as Api
 import Cardano.Api.Experimental qualified as Exp
 import Cardano.Api.Experimental.Era (convert)
 import Cardano.Api.Experimental.Tx qualified as Exp
+import Cardano.Api.Experimental.Tx.Internal.Fee (calcMinFeeRecursiveWith)
 import Cardano.Api.Genesis qualified as Genesis
 import Cardano.Api.Ledger qualified as L
 import Cardano.Api.Ledger qualified as Ledger
@@ -106,6 +107,9 @@ tests =
         , testProperty
             "Tiny surplus consumed by fee increase yields NotEnoughAda"
             prop_calcMinFeeRecursive_tiny_surplus_not_enough_ada
+        , testProperty
+            "iteration limit exhausted returns FeeCalculationDidNotConverge"
+            prop_calcMinFeeRecursive_did_not_converge
         ]
     ]
 
@@ -981,3 +985,36 @@ prop_calcMinFeeRecursive_tiny_surplus_not_enough_ada = H.property $ do
       H.assert $ actual < required
     Left err -> H.annotateShow err >> H.failure
     Right _ -> H.annotate "Expected NotEnoughAda or MinUTxONotMet but tx balanced successfully" >> H.failure
+
+-- ---------------------------------------------------------------------------
+-- Iteration limit: FeeCalculationDidNotConverge
+-- ---------------------------------------------------------------------------
+
+-- | When the maximum iteration count is set to 1 and the transaction starts
+-- with a zero fee, the first iteration updates the fee field (Case 3) but
+-- immediately exhausts the budget, so the function must return
+-- 'FeeCalculationDidNotConverge'.
+--
+-- This test uses 'calcMinFeeRecursiveWith' (the internal variant that exposes
+-- the iteration limit) to reliably exercise the error path without requiring
+-- a pathological transaction that genuinely fails to converge under the
+-- default 50-iteration limit.
+prop_calcMinFeeRecursive_did_not_converge :: Property
+prop_calcMinFeeRecursive_did_not_converge = H.property $ do
+  (unsignedTx, utxo, changeAddr) <- H.forAll $ genFundedSimpleTx Exp.ConwayEra
+  -- maxIterations = 1: the first iteration sets the fee (Case 3) and then
+  -- the counter hits 0, returning FeeCalculationDidNotConverge.
+  let result =
+        calcMinFeeRecursiveWith
+          1
+          changeAddr
+          unsignedTx
+          utxo
+          exampleProtocolParams
+          mempty
+          mempty
+          mempty
+          0
+  case result of
+    Left Exp.FeeCalculationDidNotConverge -> H.success
+    other -> H.annotateShow other >> H.failure