diff --git a/src/Test/test_attribute.jl b/src/Test/test_attribute.jl
index a8fa9faaac..a5bb796f27 100644
--- a/src/Test/test_attribute.jl
+++ b/src/Test/test_attribute.jl
@@ -393,3 +393,55 @@ function test_attribute_unsupported_constraint(model::MOI.ModelLike, ::Config)
 end
 
 version_added(::typeof(test_attribute_unsupported_constraint)) = v"1.9.0"
+
+"""
+    test_attribute_VariableBridgingCost(model::MOI.ModelLike, config::Config)
+
+Test that, for every set `S` that the model claims to support via
+`supports_add_constrained_variable(s)`, the corresponding
+[`MOI.VariableBridgingCost`](@ref) attribute returns a finite value.
+
+This is the variable-side analog of the `ConstraintBridgingCost` check in
+`_basic_constraint_test_helper`.
+
+The fallback works for most model but it may need custom method for some MOI
+layers (see https://github.com/jump-dev/MathOptInterface.jl/pull/3001#issuecomment-4468198935).
+
+This test is here to catch that.
+"""
+function test_attribute_VariableBridgingCost(
+    model::MOI.ModelLike,
+    ::Config{T},
+) where {T}
+    for S in Any[
+        MOI.GreaterThan{T},
+        MOI.LessThan{T},
+        MOI.EqualTo{T},
+        MOI.Interval{T},
+        MOI.Integer,
+        MOI.ZeroOne,
+        MOI.Semicontinuous{T},
+        MOI.Semiinteger{T},
+    ]
+        if MOI.supports_add_constrained_variable(model, S)
+            @test MOI.get(model, MOI.VariableBridgingCost{S}()) < Inf
+        end
+    end
+    for S in Any[
+        MOI.Reals,
+        MOI.Zeros,
+        MOI.Nonnegatives,
+        MOI.Nonpositives,
+        MOI.SecondOrderCone,
+        MOI.RotatedSecondOrderCone,
+        MOI.ExponentialCone,
+        MOI.PositiveSemidefiniteConeTriangle,
+    ]
+        if MOI.supports_add_constrained_variables(model, S)
+            @test MOI.get(model, MOI.VariableBridgingCost{S}()) < Inf
+        end
+    end
+    return
+end
+
+version_added(::typeof(test_attribute_VariableBridgingCost)) = v"1.52.0"
diff --git a/src/Test/test_basic_constraint.jl b/src/Test/test_basic_constraint.jl
index 0d3788d009..bacc84d8e6 100644
--- a/src/Test/test_basic_constraint.jl
+++ b/src/Test/test_basic_constraint.jl
@@ -253,6 +253,16 @@ function _basic_constraint_test_helper(
     ###
     @requires MOI.supports_constraint(model, F, S)
     ###
+    ### Test MOI.ConstraintBridgingCost
+    ###
+    # If `supports_constraint(F, S)` returns `true`, then the model must be
+    # able to handle that pair (possibly via bridging), so the bridging cost
+    # must be finite. The fallback works for most model but it may need
+    # custom method for some MOI layer (see
+    # https://github.com/jump-dev/MathOptInterface.jl/pull/3001#issuecomment-4468198935)
+    # This test is here to catch that.
+    @test MOI.get(model, MOI.ConstraintBridgingCost{F,S}()) < Inf
+    ###
     ### Test MOI.NumberOfConstraints
     ###
     @test MOI.get(model, MOI.NumberOfConstraints{F,S}()) == 0