diff --git a/src/composition/learning_networks/replace.jl b/src/composition/learning_networks/replace.jl
index 175c4b91..c9806269 100644
--- a/src/composition/learning_networks/replace.jl
+++ b/src/composition/learning_networks/replace.jl
@@ -38,6 +38,7 @@ end
         newnode_given_old,
         newmach_given_old,
         newmodel_given_old,
+        serializable,
         node::AbstractNode)
 
 **Private method.**
diff --git a/src/machines.jl b/src/machines.jl
index a1a3afc5..c194c8ae 100644
--- a/src/machines.jl
+++ b/src/machines.jl
@@ -977,14 +977,14 @@ See also [`restore!`](@ref), [`MLJBase.save`](@ref).
 """
 function serializable(mach::Machine{<:Any, C}; verbosity=1) where C
 
+    isdefined(mach, :fitresult) || throw(ERR_SERIALIZING_UNTRAINED)
+    mach.state == -1 && return mach
+
     # The next line of code makes `serializable` recursive, in the case that `mach.model`
     # is a `Composite` model: `save` duplicates the underlying learning network, which
     # involves calls to `serializable` on the old machines in the network to create the
     # new ones.
 
-    isdefined(mach, :fitresult) || throw(ERR_SERIALIZING_UNTRAINED)
-    mach.state == -1 && return mach
-
     serializable_fitresult = save(mach.model, mach.fitresult)
 
     # Duplication currenty needs to happen in two steps for this to work in case of
diff --git a/test/machines.jl b/test/machines.jl
index 7d0845c2..11062b02 100644
--- a/test/machines.jl
+++ b/test/machines.jl
@@ -508,6 +508,68 @@ end
     rm(filename)
 end
 
+# define a model with non-persistent fitresult:
+thing = []
+struct EphemeralTransformer <: Unsupervised end
+function MLJModelInterface.fit(::EphemeralTransformer, verbosity, X)
+    view = pointer(thing)
+    fitresult = (thing, view)
+    return fitresult, nothing, NamedTuple()
+end
+function MLJModelInterface.transform(::EphemeralTransformer, fitresult, X)
+    thing, view = fitresult
+    return view == pointer(thing) ? X : throw(ErrorException("dead fitresult"))
+end
+function MLJModelInterface.save(::EphemeralTransformer, fitresult)
+    thing, _ = fitresult
+    return thing
+end
+function MLJModelInterface.restore(::EphemeralTransformer, serialized_fitresult)
+    view = pointer(thing)
+    return (thing, view)
+end
+
+# commented out code just tests the transformer above has desired properties for testing:
+
+# # test model transforms:
+# model = EphemeralTransformer()
+# mach = machine(model, 42) |> fit!
+# @test MLJBase.transform(mach, 27) == 27
+
+# # direct serialization fails:
+# io = IOBuffer()
+# serialize(io, mach)
+# seekstart(io)
+# mach2 = deserialize(io)
+# @test_throws ErrorException("dead fitresult") transform(mach2, 42)
+
+@testset "serialization for model with non-persistent fitresult" begin
+    X = (; x=randn(5))
+    mach = machine(EphemeralTransformer(), X)
+    fit!(mach, verbosity=0)
+    v = MLJBase.transform(mach, X).x
+    io = IOBuffer()
+    MLJBase.save(io, serializable(mach))
+    seekstart(io)
+    mach2 = restore!(deserialize(io))
+    @test MLJBase.transform(mach2, X).x == v
+end
+
+@testset "serialization for model with non-persistent fitresult in pipeline" begin
+    # https://github.com/JuliaAI/MLJBase.jl/issues/927
+    X = (; x=randn(5))
+    pipe =  Standardizer |> EphemeralTransformer
+    X = (; x=randn(5))
+    mach = machine(pipe, X)
+    fit!(mach, verbosity=0)
+    v = MLJBase.transform(mach, X).x
+    io = IOBuffer()
+    MLJBase.save(io, serializable(mach))
+    seekstart(io)
+    mach2 = restore!(deserialize(io))
+    @test_broken MLJBase.transform(mach2, X).x == v
+end
+
 struct ReportingDynamic <: Unsupervised end
 MLJBase.fit(::ReportingDynamic, _, X) = nothing, 16, NamedTuple()
 MLJBase.transform(::ReportingDynamic,_, X) = (X, (news=42,))