diff --git a/Project.toml b/Project.toml
index 797cac5..2234904 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MLJIteration"
 uuid = "614be32b-d00c-4edb-bd02-1eb411ab5e55"
 authors = ["Anthony D. Blaom <anthony.blaom@gmail.com>"]
-version = "0.6.0"
+version = "0.6.1"
 
 [deps]
 IterationControl = "b3c1a2ee-3fec-4384-bf48-272ea71de57c"
diff --git a/src/core.jl b/src/core.jl
index df5f88b..6708ab0 100644
--- a/src/core.jl
+++ b/src/core.jl
@@ -151,3 +151,7 @@ MLJBase.predict(::EitherIteratedModel, fitresult, Xnew) =
 
 MLJBase.transform(::EitherIteratedModel, fitresult, Xnew) =
     transform(fitresult, Xnew)
+
+# here `fitresult` is a trained atomic machine:
+MLJBase.save(::EitherIteratedModel, fitresult) = MLJBase.serializable(fitresult)
+MLJBase.restore(::EitherIteratedModel, fitresult) = MLJBase.restore!(fitresult)
diff --git a/test/core.jl b/test/core.jl
index 4e75ead..2119da4 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -239,5 +239,54 @@ end
     @test iteration_parameter(model) == :n
 end
 
+# define a supervised model with ephemeral `fitresult`, but which overcomes this by
+# overloading `save`/`restore`:
+thing = []
+mutable struct EphemeralRegressor <: Deterministic
+    n::Int # dummy iteration parameter
+end
+EphemeralRegressor(; n=1) = EphemeralRegressor(n)
+function MLJBase.fit(::EphemeralRegressor, verbosity, X, y)
+    # if I serialize/deserialized `thing` then `id` below changes:
+    id = objectid(thing)
+    fitresult = (thing, id, mean(y))
+    return fitresult, nothing, NamedTuple()
+end
+function MLJBase.predict(::EphemeralRegressor, fitresult, X)
+    thing, id, μ = fitresult
+    return id == objectid(thing) ? fill(μ, nrows(X)) :
+        throw(ErrorException("dead fitresult"))
+end
+MLJBase.iteration_parameter(::EphemeralRegressor) = :n
+function MLJBase.save(::EphemeralRegressor, fitresult)
+    thing, _, μ = fitresult
+    return (thing, μ)
+end
+function MLJBase.restore(::EphemeralRegressor, serialized_fitresult)
+    thing, μ = serialized_fitresult
+    id = objectid(thing)
+    return (thing, id, μ)
+end
+
+@testset "save and restore" begin
+    #https://github.com/alan-turing-institute/MLJ.jl/issues/1099
+    X, y = (; x = rand(10)), fill(42.0, 3)
+    controls = [Step(1), NumberLimit(2)]
+    imodel = IteratedModel(
+        EphemeralRegressor(42);
+        measure=l2,
+        resampling=Holdout(),
+        controls,
+    )
+    mach = machine(imodel, X, y)
+    fit!(mach, verbosity=0)
+    io = IOBuffer()
+    MLJBase.save(io, mach)
+    seekstart(io)
+    mach2 = machine(io)
+    close(io)
+    @test MLJBase.predict(mach2, (; x = rand(2))) ≈ fill(42.0, 2)
+end
+
 end
 true