diff --git a/src/fastmcp/client/client.py b/src/fastmcp/client/client.py
index 4651edadb..c498039e9 100644
--- a/src/fastmcp/client/client.py
+++ b/src/fastmcp/client/client.py
@@ -16,7 +16,7 @@
 import mcp.types
 import pydantic_core
 from exceptiongroup import catch
-from mcp import ClientSession
+from mcp import ClientSession, McpError
 from mcp.types import (
     CancelTaskRequest,
     CancelTaskRequestParams,
@@ -514,7 +514,8 @@ async def _connect(self):
                         raise RuntimeError(
                             "Session task completed without exception but connection failed"
                         )
-                    if isinstance(exception, httpx.HTTPStatusError):
+                    # Preserve specific exception types that clients may want to handle
+                    if isinstance(exception, httpx.HTTPStatusError | McpError):
                         raise exception
                     raise RuntimeError(
                         f"Client failed to connect: {exception}"
diff --git a/src/fastmcp/client/transports.py b/src/fastmcp/client/transports.py
index a6336d123..eff3e2ba9 100644
--- a/src/fastmcp/client/transports.py
+++ b/src/fastmcp/client/transports.py
@@ -866,7 +866,11 @@ async def connect_session(
             client_read, client_write = client_streams
             server_read, server_write = server_streams
 
-            # Create a cancel scope for the server task
+            # Capture exceptions to re-raise after task group cleanup.
+            # anyio task groups can suppress exceptions when cancel_scope.cancel()
+            # is called during cleanup, so we capture and re-raise manually.
+            exception_to_raise: BaseException | None = None
+
             async with (
                 anyio.create_task_group() as tg,
                 _enter_server_lifespan(server=self.server),
@@ -892,9 +896,15 @@ async def connect_session(
                         **session_kwargs,
                     ) as client_session:
                         yield client_session
+                except BaseException as e:
+                    exception_to_raise = e
                 finally:
                     tg.cancel_scope.cancel()
 
+            # Re-raise after task group has exited cleanly
+            if exception_to_raise is not None:
+                raise exception_to_raise
+
     def __repr__(self) -> str:
         return f"<FastMCPTransport(server='{self.server.name}')>"