diff --git a/src/Bridges/Bridges.jl b/src/Bridges/Bridges.jl
index 7c0e490c56..7678d63a1d 100644
--- a/src/Bridges/Bridges.jl
+++ b/src/Bridges/Bridges.jl
@@ -222,6 +222,18 @@ function _test_structural_identical(
     return
 end
 
+_runtests_error_handler(err, ::Bool) = rethrow(err)
+
+function _runtests_error_handler(
+    err::MOI.GetAttributeNotAllowed{MOI.ConstraintFunction},
+    cannot_unbridge::Bool,
+)
+    if cannot_unbridge
+        return  # This error is expected. Do nothing.
+    end
+    return rethrow(err)
+end
+
 """
     runtests(
         Bridge::Type{<:AbstractBridge},
@@ -305,13 +317,8 @@ function runtests(
             set = try
                 MOI.get(model, MOI.ConstraintSet(), ci)
             catch err
-                # Could be thrown by `unbridged_function`
-                if cannot_unbridge &&
-                   err isa MOI.GetAttributeNotAllowed{MOI.ConstraintFunction}
-                    continue
-                else
-                    rethrow(err)
-                end
+                _runtests_error_handler(err, cannot_unbridge)
+                continue
             end
             for attr in (MOI.ConstraintPrimalStart(), MOI.ConstraintDualStart())
                 if MOI.supports(model, attr, MOI.ConstraintIndex{F,S})
diff --git a/test/Bridges/Variable/zeros.jl b/test/Bridges/Variable/zeros.jl
index 7dad8da30c..a531b199ef 100644
--- a/test/Bridges/Variable/zeros.jl
+++ b/test/Bridges/Variable/zeros.jl
@@ -46,6 +46,30 @@ function test_runtests()
     return
 end
 
+function test_bridge_error_handler()
+    for (err, flag) in (
+        ErrorException("abc") => false,
+        MOI.GetAttributeNotAllowed(MOI.ObjectiveSense()) => false,
+        MOI.GetAttributeNotAllowed(MOI.ConstraintFunction()) => true,
+    )
+        @test_throws err try
+            @assert false
+        catch
+            MOI.Bridges._runtests_error_handler(err, false)
+        end
+        if flag
+            @test MOI.Bridges._runtests_error_handler(err, true) === nothing
+        else
+            @test_throws err try
+                @assert false
+            catch
+                MOI.Bridges._runtests_error_handler(err, true)
+            end
+        end
+    end
+    return
+end
+
 function test_zeros()
     mock = MOI.Utilities.MockOptimizer(MOI.Utilities.Model{Float64}())
     bridged_mock = MOI.Bridges.Variable.Zeros{Float64}(mock)