diff --git a/src/librustc/traits/error_reporting/mod.rs b/src/librustc/traits/error_reporting/mod.rs
index d1c369d0abbf3..cdb50779e00cc 100644
--- a/src/librustc/traits/error_reporting/mod.rs
+++ b/src/librustc/traits/error_reporting/mod.rs
@@ -919,17 +919,29 @@ impl<'a, 'tcx> InferCtxt<'a, 'tcx> {
                 report_object_safety_error(self.tcx, span, did, violations)
             }
 
-            // already reported in the query
-            ConstEvalFailure(err) => {
-                if let ErrorHandled::TooGeneric = err {
-                    // Silence this error, as it can be produced during intermediate steps
-                    // when a constant is not yet able to be evaluated (but will be later).
-                    return;
-                }
-                self.tcx.sess.delay_span_bug(
-                    span,
-                    &format!("constant in type had an ignored error: {:?}", err),
-                );
+            ConstEvalFailure(ErrorHandled::TooGeneric) => {
+                // In this instance, we have a const expression containing an unevaluated
+                // generic parameter. We have no idea whether this expression is valid or
+                // not (e.g. it might result in an error), but we don't want to just assume
+                // that it's okay, because that might result in post-monomorphisation time
+                // errors. The onus is really on the caller to provide values that it can
+                // prove are well-formed.
+                let mut err = self
+                    .tcx
+                    .sess
+                    .struct_span_err(span, "constant expression depends on a generic parameter");
+                // FIXME(const_generics): we should suggest to the user how they can resolve this
+                // issue. However, this is currently not actually possible
+                // (see https://github.com/rust-lang/rust/issues/66962#issuecomment-575907083).
+                err.note("this may fail depending on what value the parameter takes");
+                err
+            }
+
+            // Already reported in the query.
+            ConstEvalFailure(ErrorHandled::Reported) => {
+                self.tcx
+                    .sess
+                    .delay_span_bug(span, &format!("constant in type had an ignored error"));
                 return;
             }
 
diff --git a/src/test/ui/const-generics/array-size-in-generic-struct-param.rs b/src/test/ui/const-generics/array-size-in-generic-struct-param.rs
index f3be7b56db589..d996bf56fcc10 100644
--- a/src/test/ui/const-generics/array-size-in-generic-struct-param.rs
+++ b/src/test/ui/const-generics/array-size-in-generic-struct-param.rs
@@ -1,10 +1,9 @@
-// run-pass
-
 #![feature(const_generics)]
 //~^ WARN the feature `const_generics` is incomplete and may cause the compiler to crash
 
 #[allow(dead_code)]
-struct ArithArrayLen<const N: usize>([u32; 0 + N]); // ok
+struct ArithArrayLen<const N: usize>([u32; 0 + N]);
+//~^ ERROR constant expression depends on a generic parameter
 
 #[derive(PartialEq, Eq)]
 struct Config {
@@ -12,7 +11,7 @@ struct Config {
 }
 
 struct B<const CFG: Config> {
-    arr: [u8; CFG.arr_size], // ok
+    arr: [u8; CFG.arr_size], //~ ERROR constant expression depends on a generic parameter
 }
 
 const C: Config = Config { arr_size: 5 };
diff --git a/src/test/ui/const-generics/array-size-in-generic-struct-param.stderr b/src/test/ui/const-generics/array-size-in-generic-struct-param.stderr
index 274f97697029e..6ae70c493b1dd 100644
--- a/src/test/ui/const-generics/array-size-in-generic-struct-param.stderr
+++ b/src/test/ui/const-generics/array-size-in-generic-struct-param.stderr
@@ -1,8 +1,26 @@
 warning: the feature `const_generics` is incomplete and may cause the compiler to crash
-  --> $DIR/array-size-in-generic-struct-param.rs:3:12
+  --> $DIR/array-size-in-generic-struct-param.rs:1:12
    |
 LL | #![feature(const_generics)]
    |            ^^^^^^^^^^^^^^
    |
    = note: `#[warn(incomplete_features)]` on by default
 
+error: constant expression depends on a generic parameter
+  --> $DIR/array-size-in-generic-struct-param.rs:5:38
+   |
+LL | struct ArithArrayLen<const N: usize>([u32; 0 + N]);
+   |                                      ^^^^^^^^^^^^
+   |
+   = note: this may fail depending on what value the parameter takes
+
+error: constant expression depends on a generic parameter
+  --> $DIR/array-size-in-generic-struct-param.rs:14:5
+   |
+LL |     arr: [u8; CFG.arr_size],
+   |     ^^^^^^^^^^^^^^^^^^^^^^^
+   |
+   = note: this may fail depending on what value the parameter takes
+
+error: aborting due to 2 previous errors
+