diff --git a/src/Utilities/matrix_of_constraints.jl b/src/Utilities/matrix_of_constraints.jl
index 503b149110..43d4f80448 100644
--- a/src/Utilities/matrix_of_constraints.jl
+++ b/src/Utilities/matrix_of_constraints.jl
@@ -707,10 +707,11 @@ function MOI.modify(
     ci::MOI.ConstraintIndex,
     change::Union{MOI.ScalarConstantChange,MOI.VectorConstantChange},
 )
-    try
+    ret =
         modify_constants(model.constants, rows(model, ci), change.new_constant)
-    catch
-        throw(MOI.ModifyConstraintNotAllowed(ci, change))
+    if ret == _ModifyConstantsNotImplemented()
+        msg = "`modify_constants` is not implemented for `$(typeof(model.constants))`"
+        throw(MOI.ModifyConstraintNotAllowed(ci, change, msg))
     end
     return
 end
@@ -738,6 +739,15 @@ function MOI.modify(
     return
 end
 
+# See https://github.com/jump-dev/MathOptInterface.jl/pull/2976
+# Ideally we would have made it so that `modify_constants` operated like
+# `modify_coefficients` and returned a `Bool` indicating success. But we didn't,
+# so here's a hacky work-around to catch if the method is not implemented
+# without resorting to a try-catch.
+struct _ModifyConstantsNotImplemented end
+
+modify_constants(args...) = _ModifyConstantsNotImplemented()
+
 function modify_constants(
     b::AbstractVector{T},
     row::Integer,
diff --git a/test/Utilities/test_matrix_of_constraints.jl b/test/Utilities/test_matrix_of_constraints.jl
index 256fb2a931..f545c2b3b9 100644
--- a/test/Utilities/test_matrix_of_constraints.jl
+++ b/test/Utilities/test_matrix_of_constraints.jl
@@ -763,6 +763,31 @@ function test_modify_vectorsets()
     return
 end
 
+function test_modify_constants_bounds_error()
+    model = _new_VectorSets()
+    src = MOI.Utilities.Model{Int}()
+    x = MOI.add_variables(src, 2)
+    c = MOI.add_constraint(
+        src,
+        MOI.VectorAffineFunction{Int}(
+            MOI.VectorAffineTerm.(1, MOI.ScalarAffineTerm.(1, x)),
+            [1, 3],
+        ),
+        MOI.SecondOrderCone(2),
+    )
+    index_map = MOI.copy_to(model, src)
+    resize!(model.constraints.constants, 0)
+    @test_throws(
+        BoundsError,
+        MOI.modify(
+            model.constraints,
+            index_map[c],
+            MOI.VectorConstantChange([4, 5]),
+        ),
+    )
+    return
+end
+
 function test_modify_set_constants()
     model = MOI.Utilities.Model{Float64}()
     x = MOI.add_variables(model, 3)
@@ -789,8 +814,13 @@ function test_modify_set_constants()
     index_map = MOI.copy_to(cache, model)
     ci = index_map[p_ref]
     change = MOI.VectorConstantChange([4.0, 5.0, 6.0])
+    constants_type = typeof(cache.constraints.constants)
     @test_throws(
-        MOI.ModifyConstraintNotAllowed(ci, change),
+        MOI.ModifyConstraintNotAllowed(
+            ci,
+            change,
+            "`modify_constants` is not implemented for `$constants_type`",
+        ),
         MOI.modify(cache, ci, change),
     )
     return