diff --git a/src/constraint.jl b/src/constraint.jl
index 7908896..47f2e42 100644
--- a/src/constraint.jl
+++ b/src/constraint.jl
@@ -128,11 +128,34 @@ function _concrete(
         S,
     )
 end
+
+# Dispatched assertion that mirrors `_concrete`: a bridge listed in
+# `bridges(S)` must, per MOI's contract on `concrete_bridge_type`, support its
+# source set before `concrete_bridge_type` (and the downstream
+# `added_*_types`) can be called. We dispatch on the bridge supertype so the
+# right `supports_*` method is queried.
+function _supports(
+    bridge_type::Type{<:MOI.Bridges.Variable.AbstractBridge},
+    S::Type{<:MOI.AbstractSet},
+)
+    return MOI.Bridges.Variable.supports_constrained_variable(bridge_type, S)
+end
+function _supports(
+    bridge_type::Type{<:MOI.Bridges.Constraint.AbstractBridge},
+    S::Type{<:MOI.AbstractSet},
+)
+    return MOI.supports_constraint(bridge_type, MOI.VectorOfVariables, S)
+end
 function bridgeable(c::JuMP.AbstractConstraint, S::Type{<:MOI.AbstractSet})
     bridge_types = bridges(S)
     for bridge_type in bridge_types
         BT, T = bridge_type
         c = BridgeableConstraint(c, BT; coefficient_type = T)
+        # `concrete_bridge_type` documents that it may only be called when
+        # the bridge's `supports_*` predicate is `true`.
+        # Otherwise, it just return `BT{T}` for which `added_constrained_variable_types`
+        # is not implemented and that gives cryptic error.
+        @assert _supports(BT{T}, S)
         concrete_bridge_type = _concrete(BT{T}, S)
         for (ST,) in
             MOI.Bridges.added_constrained_variable_types(concrete_bridge_type)
@@ -162,6 +185,12 @@ function bridgeable(
     for bridge_type in bridge_types
         BT, T = bridge_type
         c = BridgeableConstraint(c, BT, coefficient_type = T)
+        # Same invariant as the variable version above: a bridge listed in
+        # `bridges(F, S)` must actually support `F`-in-`S` per MOI's contract
+        # on `concrete_bridge_type`. Failing this assertion means the call
+        # site listed a bridge in `bridges(F, S)` that does not bridge `F` in
+        # `S`.
+        @assert MOI.supports_constraint(BT{T}, F, S)
         concrete_bridge_type =
             MOI.Bridges.Constraint.concrete_bridge_type(BT{T}, F, S)
         for (ST,) in
diff --git a/test/bridgeable.jl b/test/bridgeable.jl
new file mode 100644
index 0000000..ea0e5a7
--- /dev/null
+++ b/test/bridgeable.jl
@@ -0,0 +1,49 @@
+module TestBridgeable
+
+using Test
+using JuMP
+using PolyJuMP
+import MathOptInterface as MOI
+
+# These sets deliberately list bridges that do not support them.
+struct UnsupportedSet{B} <: MOI.AbstractVectorSet end
+
+function PolyJuMP.bridges(::Type{UnsupportedSet{B}}) where {B}
+    return Tuple{Type,Type}[(B, Float64)]
+end
+
+function PolyJuMP.bridges(
+    ::Type{<:MOI.AbstractVectorFunction},
+    S::Type{<:UnsupportedSet},
+)
+    return PolyJuMP.bridges(S)
+end
+
+function test_supports()
+    VB = MOI.Bridges.Variable.ZerosBridge{Float64}
+    @test PolyJuMP._supports(VB, MOI.Zeros)
+    @test !PolyJuMP._supports(VB, MOI.Nonnegatives)
+    CB = MOI.Bridges.Constraint.ScalarizeBridge{Float64}
+    @test PolyJuMP._supports(CB, MOI.Zeros)
+    @test !PolyJuMP._supports(CB, MOI.SecondOrderCone)
+end
+
+function test_unsupported_bridges()
+    c = JuMP.VectorConstraint([1.0], MOI.Zeros(1))
+    VS = UnsupportedSet{MOI.Bridges.Variable.ZerosBridge}
+    @test_throws AssertionError PolyJuMP.bridgeable(c, VS)
+    CS = UnsupportedSet{MOI.Bridges.Constraint.ScalarizeBridge}
+    @test_throws AssertionError PolyJuMP.bridgeable(c, CS)
+    @test_throws AssertionError PolyJuMP.bridgeable(
+        c,
+        MOI.VectorOfVariables,
+        CS,
+    )
+end
+
+@testset "Bridge support" begin
+    test_supports()
+    test_unsupported_bridges()
+end
+
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index bb6e841..d4627aa 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,7 @@
 include("polymodule.jl")
 include("variable.jl")
 include("constraint.jl")
+include("bridgeable.jl")
 include("functions.jl")
 include("model.jl")
 include("to_polynomial.jl")
diff --git a/test/testpolymodule.jl b/test/testpolymodule.jl
index 74011f7..041c121 100644
--- a/test/testpolymodule.jl
+++ b/test/testpolymodule.jl
@@ -36,6 +36,13 @@ function PolyJuMP.bridges(
         PolyJuMP.coefficient_type_or_float(F),
     )]
 end
+function MOI.supports_constraint(
+    ::Type{<:DummyNonNegBridge},
+    ::Type{<:MOI.AbstractVectorFunction},
+    ::Type{<:NonNeg},
+)
+    return true
+end
 function MOI.Bridges.added_constrained_variable_types(
     ::Type{<:DummyNonNegBridge},
 )