diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,10 @@
 # Revision history for th-abstraction
 
+## 0.4.4.0 -- 2022.07.23
+* Support free variable substitution and infix resolution for
+  `PromotedInfixT` and `PromotedUInfixT` on `template-haskell-2.19.0.0` or
+  later.
+
 ## 0.4.3.0 -- 2021.08.30
 * Make `applySubstitution` avoid capturing type variable binders when
   substituting into `forall`s.
diff --git a/src/Language/Haskell/TH/Datatype.hs b/src/Language/Haskell/TH/Datatype.hs
--- a/src/Language/Haskell/TH/Datatype.hs
+++ b/src/Language/Haskell/TH/Datatype.hs
@@ -1306,6 +1306,16 @@
          ForallVisT `fmap` mapM resolve_tvb_syns tvbs
                       `ap` resolveTypeSynonyms body
 #endif
+#if MIN_VERSION_template_haskell(2,19,0)
+       PromotedInfixT t1 n t2 -> do
+         t1' <- resolveTypeSynonyms t1
+         t2' <- resolveTypeSynonyms t2
+         return $ PromotedInfixT t1' n t2'
+       PromotedUInfixT t1 n t2 -> do
+         t1' <- resolveTypeSynonyms t1
+         t2' <- resolveTypeSynonyms t2
+         return $ PromotedUInfixT t1' n t2'
+#endif
        _ -> defaultCase f
 
 -- | Expand all of the type synonyms in a 'TypeArg'.
@@ -1493,29 +1503,41 @@
 resolveInfixT (ForallVisT vs t) = ForallVisT <$> traverse (traverseTVKind resolveInfixT) vs
                                              <*> resolveInfixT t
 # endif
+# if MIN_VERSION_template_haskell(2,19,0)
+resolveInfixT (PromotedInfixT l o r)
+                                = promotedT o `appT` resolveInfixT l `appT` resolveInfixT r
+resolveInfixT t@PromotedUInfixT{}
+                                = resolveInfixT =<< resolveInfixT1 (gatherUInfixT t)
+# endif
 resolveInfixT t                 = return t
 
 gatherUInfixT :: Type -> InfixList
-gatherUInfixT (UInfixT l o r) = ilAppend (gatherUInfixT l) o (gatherUInfixT r)
+gatherUInfixT (UInfixT l o r)         = ilAppend (gatherUInfixT l) o False (gatherUInfixT r)
+# if MIN_VERSION_template_haskell(2,19,0)
+gatherUInfixT (PromotedUInfixT l o r) = ilAppend (gatherUInfixT l) o True  (gatherUInfixT r)
+# endif
 gatherUInfixT t = ILNil t
 
 -- This can fail due to incompatible fixities
 resolveInfixT1 :: InfixList -> TypeQ
 resolveInfixT1 = go []
   where
-    go :: [(Type,Name,Fixity)] -> InfixList -> TypeQ
-    go ts (ILNil u) = return (foldl (\acc (l,o,_) -> ConT o `AppT` l `AppT` acc) u ts)
-    go ts (ILCons l o r) =
+    go :: [(Type,Name,Bool,Fixity)] -> InfixList -> TypeQ
+    go ts (ILNil u) = return (foldl (\acc (l,o,p,_) -> mkConT p o `AppT` l `AppT` acc) u ts)
+    go ts (ILCons l o p r) =
       do ofx <- fromMaybe defaultFixity <$> reifyFixityCompat o
-         let push = go ((l,o,ofx):ts) r
+         let push = go ((l,o,p,ofx):ts) r
          case ts of
-           (l1,o1,o1fx):ts' ->
+           (l1,o1,p1,o1fx):ts' ->
              case compareFixity o1fx ofx of
-               Just True  -> go ((ConT o1 `AppT` l1 `AppT` l, o, ofx):ts') r
+               Just True  -> go ((mkConT p1 o1 `AppT` l1 `AppT` l, o, p, ofx):ts') r
                Just False -> push
                Nothing    -> fail (precedenceError o1 o1fx o ofx)
            _ -> push
 
+    mkConT :: Bool -> Name -> Type
+    mkConT promoted = if promoted then PromotedT else ConT
+
     compareFixity :: Fixity -> Fixity -> Maybe Bool
     compareFixity (Fixity n1 InfixL) (Fixity n2 InfixL) = Just (n1 >= n2)
     compareFixity (Fixity n1 InfixR) (Fixity n2 InfixR) = Just (n1 >  n2)
@@ -1532,11 +1554,17 @@
       nameBase o2 ++ "’ [" ++ showFixity ofx2 ++
       "] in the same infix type expression"
 
-data InfixList = ILCons Type Name InfixList | ILNil Type
+data InfixList
+  = ILCons Type      -- The first argument to the type operator
+           Name      -- The name of the infix type operator
+           Bool      -- 'True' if this is a promoted infix data constructor,
+                     -- 'False' otherwise
+           InfixList -- The rest of the infix applications to resolve
+  | ILNil Type
 
-ilAppend :: InfixList -> Name -> InfixList -> InfixList
-ilAppend (ILNil l)         o r = ILCons l o r
-ilAppend (ILCons l1 o1 r1) o r = ILCons l1 o1 (ilAppend r1 o r)
+ilAppend :: InfixList -> Name -> Bool -> InfixList -> InfixList
+ilAppend (ILNil l)            o p r = ILCons l o p r
+ilAppend (ILCons l1 o1 p1 r1) o p r = ILCons l1 o1 p1 (ilAppend r1 o p r)
 
 #else
 -- older template-haskell packages don't have UInfixT
@@ -1788,6 +1816,12 @@
         ForallVisT tvs'
                    (applySubstitution subst' t)
 #endif
+#if MIN_VERSION_template_haskell(2,19,0)
+      go (PromotedInfixT l c r)
+                         = PromotedInfixT (go l) c (go r)
+      go (PromotedUInfixT l c r)
+                         = PromotedUInfixT (go l) c (go r)
+#endif
       go t               = t
 
       subst_tvbs :: [TyVarBndr_ flag] -> (Map Name Type -> a) -> a
@@ -1813,6 +1847,12 @@
 #if MIN_VERSION_template_haskell(2,16,0)
       ForallVisT tvs t'
                     -> fvs_under_forall tvs (freeVariables t')
+#endif
+#if MIN_VERSION_template_haskell(2,19,0)
+      PromotedInfixT l _ r
+                    -> freeVariables l `union` freeVariables r
+      PromotedUInfixT l _ r
+                    -> freeVariables l `union` freeVariables r
 #endif
       _             -> []
     where
diff --git a/test/Harness.hs b/test/Harness.hs
--- a/test/Harness.hs
+++ b/test/Harness.hs
@@ -40,7 +40,7 @@
 validate equate x y = either fail (\_ -> [| return () |]) (equate x y)
 
 -- | If the arguments are equal up to renaming return @'Right' ()@,
--- otherwise return a string exlaining the mismatch.
+-- otherwise return a string explaining the mismatch.
 equateDI :: DatatypeInfo -> DatatypeInfo -> Either String ()
 equateDI dat1 dat2 =
   do check "datatypeName"          (nameBase . datatypeName)    dat1 dat2
@@ -75,7 +75,7 @@
      check (lbl ++ " equality") asEqualPred pred1 pred2
 
 -- | If the arguments are equal up to renaming return @'Right' ()@,
--- otherwise return a string exlaining the mismatch.
+-- otherwise return a string explaining the mismatch.
 equateCI :: ConstructorInfo -> ConstructorInfo -> Either String ()
 equateCI con1 con2 =
   do check "constructorName"       (nameBase . constructorName) con1 con2
diff --git a/test/Main.hs b/test/Main.hs
--- a/test/Main.hs
+++ b/test/Main.hs
@@ -92,8 +92,11 @@
      t80Test
 #endif
 #if MIN_VERSION_template_haskell(2,11,0)
-     t79Test
+     t79TestA
 #endif
+#if MIN_VERSION_template_haskell(2,19,0)
+     t79TestB
+#endif
 #if __GLASGOW_HASKELL__ >= 800
      t37Test
      polyKindedExTyvarTest
@@ -829,6 +832,10 @@
        test (ParensT (idAppT $ ConT ''Int))
             (ConT ''Int)
 #endif
+#if MIN_VERSION_template_haskell(2,19,0)
+       test (PromotedInfixT (idAppT $ ConT ''Int) '(:^:) (idAppT $ ConT ''Int))
+            (PromotedInfixT (ConT ''Int) '(:^:) (ConT ''Int))
+#endif
        [| return () |])
 
 t66Test :: IO ()
@@ -880,12 +887,30 @@
 #endif
 
 #if MIN_VERSION_template_haskell(2,11,0)
-t79Test :: IO ()
-t79Test =
+t79TestA :: IO ()
+t79TestA =
   $(do let [a,b,c]  = map mkName ["a","b","c"]
            t        = ForallT [kindedTVSpecified a (UInfixT (VarT b) ''(:+:) (VarT c))] []
                               (ConT ''())
            expected = ForallT [kindedTVSpecified a (ConT ''(:+:) `AppT` VarT b `AppT` VarT c)] []
+                              (ConT ''())
+       actual <- resolveInfixT t
+       unless (expected == actual) $
+         fail $ "resolveInfixT does not recur into the kinds of "
+             ++ "ForallT type variable binders: "
+             ++ unlines [ "Expected: " ++ pprint expected
+                        , "Actual:   " ++ pprint actual
+                        ]
+       [| return () |])
+#endif
+
+#if MIN_VERSION_template_haskell(2,19,0)
+t79TestB :: IO ()
+t79TestB =
+  $(do let [a,b,c]  = map mkName ["a","b","c"]
+           t        = ForallT [kindedTVSpecified a (PromotedUInfixT (VarT b) '(:^:) (VarT c))] []
+                              (ConT ''())
+           expected = ForallT [kindedTVSpecified a (PromotedT '(:^:) `AppT` VarT b `AppT` VarT c)] []
                               (ConT ''())
        actual <- resolveInfixT t
        unless (expected == actual) $
diff --git a/test/Types.hs b/test/Types.hs
--- a/test/Types.hs
+++ b/test/Types.hs
@@ -71,6 +71,8 @@
 
 type (:+:) = Either
 
+data MyPair a b = a :^: b
+
 -- Data families
 data family T43Fam
 
diff --git a/th-abstraction.cabal b/th-abstraction.cabal
--- a/th-abstraction.cabal
+++ b/th-abstraction.cabal
@@ -1,5 +1,5 @@
 name:                th-abstraction
-version:             0.4.3.0
+version:             0.4.4.0
 synopsis:            Nicer interface for reified information about data types
 description:         This package normalizes variations in the interface for
                      inspecting datatype information via Template Haskell
@@ -17,7 +17,7 @@
 build-type:          Simple
 extra-source-files:  ChangeLog.md README.md
 cabal-version:       >=1.10
-tested-with:         GHC==9.2.*, GHC==9.0.1, GHC==8.10.7, GHC==8.8.4, GHC==8.6.5, GHC==8.4.4, GHC==8.2.2, GHC==8.0.2, GHC==7.10.3, GHC==7.8.4, GHC==7.6.3, GHC==7.4.2, GHC==7.2.2, GHC==7.0.4
+tested-with:         GHC==9.2.2, GHC==9.0.2, GHC==8.10.7, GHC==8.8.4, GHC==8.6.5, GHC==8.4.4, GHC==8.2.2, GHC==8.0.2, GHC==7.10.3, GHC==7.8.4, GHC==7.6.3, GHC==7.4.2, GHC==7.2.2, GHC==7.0.4
 
 source-repository head
   type: git
@@ -29,7 +29,7 @@
   other-modules:       Language.Haskell.TH.Datatype.Internal
   build-depends:       base             >=4.3   && <5,
                        ghc-prim,
-                       template-haskell >=2.5   && <2.19,
+                       template-haskell >=2.5   && <2.20,
                        containers       >=0.4   && <0.7
   hs-source-dirs:      src
   default-language:    Haskell2010