diff --git a/amaranth/lib/data.py b/amaranth/lib/data.py
index c33771f9c..28ac905a2 100644
--- a/amaranth/lib/data.py
+++ b/amaranth/lib/data.py
@@ -775,6 +775,9 @@ def eq(self, other):
         :class:`.Assign`
             :py:`self.as_value().eq(other)`
         """
+        if isinstance(other, ValueCastable):
+            if not self.shape() == Layout.cast(other.shape()):
+                raise TypeError(f"Cannot assign value with shape {other.shape()} to view with layout {self.shape()}")
         return self.as_value().eq(other)
 
     def __getitem__(self, key):
diff --git a/amaranth/lib/enum.py b/amaranth/lib/enum.py
index 0beadacb7..043a0e5b7 100644
--- a/amaranth/lib/enum.py
+++ b/amaranth/lib/enum.py
@@ -248,6 +248,9 @@ def eq(self, other):
         :class:`Assign`
             ``self.as_value().eq(other)``
         """
+        if isinstance(other, ValueCastable):
+            if not self.shape() == other.shape():
+                raise TypeError(f"Cannot assign value with shape {other.shape()} to value with shape {self.shape()}")
         return self.as_value().eq(other)
 
     def __add__(self, other):
diff --git a/amaranth/lib/wiring.py b/amaranth/lib/wiring.py
index ef0a7499d..67ddcdb7e 100644
--- a/amaranth/lib/wiring.py
+++ b/amaranth/lib/wiring.py
@@ -2,6 +2,7 @@
 import enum
 import re
 import warnings
+import inspect
 try:
     import annotationlib # py3.14+
 except ImportError:
@@ -1562,21 +1563,26 @@ def connect(m, *args, **kwargs):
         (out_path, out_member), = out_kind
         for (in_path, in_member) in in_kind:
             def connect_value(*, out_path, in_path, src_loc_at):
-                in_value = Value.cast(_traverse_path(in_path, objects))
-                out_value = Value.cast(_traverse_path(out_path, objects))
-                assert type(in_value) in (Const, Signal)
+                in_value = _traverse_path(in_path, objects)
+                out_value = _traverse_path(out_path, objects)
                 # If the input is a constant, only a constant may be connected to it. Ensure that
                 # this is the case.
+                try:
+                    in_value = Const.cast(in_value)
+                except TypeError:
+                    pass
                 if type(in_value) is Const:
                     # If the output is not a constant, the connection is illegal.
-                    if type(out_value) is not Const:
+                    try:
+                        out_value = Const.cast(out_value)
+                    except TypeError:
                         raise ConnectionError(
                             f"Cannot connect input member {_format_path(in_path)} that has "
                             f"a constant value {in_value.value!r} to an output member "
                             f"{_format_path(out_path)} that has a varying value")
                     # If the output is a constant, the connection is legal only if the value is
                     # the same for both the input and the output.
-                    if type(out_value) is Const and in_value.value != out_value.value:
+                    if in_value.value != out_value.value:
                         raise ConnectionError(
                             f"Cannot connect input member {_format_path(in_path)} that has "
                             f"a constant value {in_value.value!r} to an output member "
@@ -1586,8 +1592,24 @@ def connect_value(*, out_path, in_path, src_loc_at):
                     # value (which is constant) is consistent with a connection that would have
                     # been made.
                     return
-                # A connection that is made at this point is guaranteed to be valid.
-                connections.append(in_value.eq(out_value, src_loc_at=src_loc_at + 1))
+                # If the input is a ValueCastable, it must implement `eq()`.
+                try:
+                    eq = in_value.eq
+                except AttributeError:
+                    raise ConnectionError(
+                        f"Cannot connect input member {_format_path(in_path)} because the input "
+                        f"value {in_value!r} does not support assignment")
+                # The `eq()` method may take a `src_loc_at` argument; provide it if it does.
+                if 'src_loc_at' in inspect.signature(eq).parameters:
+                    kwargs = {'src_loc_at': src_loc_at + 1}
+                else:
+                    kwargs = {}
+                try:
+                    connections.append(eq(out_value, **kwargs))
+                except Exception as e:
+                    raise ConnectionError(
+                        f"Cannot connect input member {_format_path(in_path)} to output member "
+                        f"{_format_path(out_path)} because assignment failed") from e
             def connect_dimensions(dimensions, *, out_path, in_path, src_loc_at):
                 if not dimensions:
                     return connect_value(out_path=out_path, in_path=in_path, src_loc_at=src_loc_at)
diff --git a/tests/test_lib_wiring.py b/tests/test_lib_wiring.py
index eb2639047..9fcce5dce 100644
--- a/tests/test_lib_wiring.py
+++ b/tests/test_lib_wiring.py
@@ -851,6 +851,24 @@ class Cycle(enum.Enum, shape=2):
                     q=NS(signature=Signature({"a": In(Cycle)}),
                          a=Signal(Cycle)))
 
+    def test_shape_mismatch_layout(self):
+        class LastDelimited(data.Struct):
+            data: 8
+            last: 1
+        class FirstDelimited(data.Struct):
+            data: 8
+            first: 1
+
+        m = Module()
+        with self.assertRaisesRegex(ConnectionError,
+                r"^Cannot connect input member 'q\.a' to output member 'p\.a' because assignment "
+                r"failed$"):
+            connect(m,
+                    p=NS(signature=Signature({"a": Out(LastDelimited)}),
+                         a=Signal(LastDelimited)),
+                    q=NS(signature=Signature({"a": In(FirstDelimited)}),
+                         a=Signal(FirstDelimited)))
+
     def test_init_mismatch(self):
         m = Module()
         with self.assertRaisesRegex(ConnectionError,