diff --git a/src/constraints.jl b/src/constraints.jl
index a941ea80e8a..6e13bb3cee5 100644
--- a/src/constraints.jl
+++ b/src/constraints.jl
@@ -747,6 +747,11 @@ function add_constraint(
     con::BridgeableConstraint,
     name::String = "",
 )
+    # Like the generic `add_constraint`, convert to the value type of the model.
+    # This is needed for constraints that reach this method without going through
+    # the `model_convert` call of the `@constraint` macro, e.g. constraints built
+    # in `add_constraint` by an extension that delays their construction.
+    con = model_convert(model, con)
     add_bridge(model, con.bridge_type; coefficient_type = con.coefficient_type)
     return add_constraint(model, con.constraint, name)
 end
diff --git a/src/macros.jl b/src/macros.jl
index cb94efa0b0c..724d2f4c568 100644
--- a/src/macros.jl
+++ b/src/macros.jl
@@ -323,10 +323,18 @@ function model_convert(model::AbstractModel, α::Number)
 end
 
 function model_convert(model::AbstractModel, con::BridgeableConstraint)
+    # The bridge `coefficient_type` is set by `build_constraint` which does not
+    # have access to the model. We convert it to the value type of the model
+    # (keeping the same real/complex flavor) just like we convert the
+    # coefficients of the function. This is needed so that, e.g., the bridges
+    # registered for a `GenericModel{T}` with `T != Float64` use `T`.
     return BridgeableConstraint(
         model_convert(model, con.constraint),
         con.bridge_type;
-        con.coefficient_type,
+        coefficient_type = _complex_convert_type(
+            value_type(typeof(model)),
+            con.coefficient_type,
+        ),
     )
 end
 
diff --git a/test/test_model.jl b/test/test_model.jl
index cb11ffa7bb5..12548356881 100644
--- a/test/test_model.jl
+++ b/test/test_model.jl
@@ -436,7 +436,59 @@ function test_macro_bridgeable()
     model = Model()
     @variable(model, x)
     @constraint(model, x in BridgeMe{Int,Nonnegative}(Nonnegative()))
-    @test NonnegativeBridge{Int} in model.bridge_types
+    # `model_convert` normalizes the bridge coefficient type to the value type of
+    # the model (`Float64`), even though `BridgeMe` requested `Int`.
+    @test NonnegativeBridge{Float64} in model.bridge_types
+    @test !(NonnegativeBridge{Int} in model.bridge_types)
+end
+
+function test_model_convert_bridgeable_coefficient_type()
+    model = GenericModel{BigFloat}()
+    @variable(model, x)
+    constraint = ScalarConstraint(x, Nonnegative())
+    # A real coefficient type is converted to the value type of the model.
+    con = BridgeableConstraint(
+        constraint,
+        NonnegativeBridge;
+        coefficient_type = Int,
+    )
+    @test model_convert(model, con).coefficient_type == BigFloat
+    # A complex coefficient type keeps its complex flavor.
+    con = BridgeableConstraint(
+        constraint,
+        NonnegativeBridge;
+        coefficient_type = Complex{Int},
+    )
+    @test model_convert(model, con).coefficient_type == Complex{BigFloat}
+    return
+end
+
+function test_macro_bridgeable_generic_value_type()
+    model = GenericModel{BigFloat}()
+    @variable(model, x)
+    @constraint(model, x in BridgeMe{Int,Nonnegative}(Nonnegative()))
+    @test NonnegativeBridge{BigFloat} in model.bridge_types
+    @test !(NonnegativeBridge{Int} in model.bridge_types)
+    return
+end
+
+function test_add_constraint_bridgeable_model_convert()
+    # `add_constraint` applies `model_convert`, so a `BridgeableConstraint` added
+    # directly (not via the `@constraint` macro, e.g. by an extension that delays
+    # the construction of the constraint) also gets its coefficient type
+    # converted to the value type of the model.
+    model = GenericModel{BigFloat}()
+    @variable(model, x)
+    constraint = ScalarConstraint(x, Nonnegative())
+    bc = BridgeableConstraint(
+        constraint,
+        NonnegativeBridge;
+        coefficient_type = Int,
+    )
+    add_constraint(model, bc)
+    @test NonnegativeBridge{BigFloat} in model.bridge_types
+    @test !(NonnegativeBridge{Int} in model.bridge_types)
+    return
 end
 
 function test_bridges_add_bridgeable_con_set_optimizer()