diff --git a/mcp/streamable.go b/mcp/streamable.go
index d6452b28..5a6d828e 100644
--- a/mcp/streamable.go
+++ b/mcp/streamable.go
@@ -1376,6 +1376,10 @@ func (c *streamableServerConn) Close() error {
 // A StreamableClientTransport is a [Transport] that can communicate with an MCP
 // endpoint serving the streamable HTTP transport defined by the 2025-03-26
 // version of the spec.
+//
+// If the server terminates the session (returning 404 Not Found), subsequent
+// operations on the [ClientSession] will return an error wrapping
+// [ErrSessionMissing].
 type StreamableClientTransport struct {
 	Endpoint   string
 	HTTPClient *http.Client
@@ -1493,16 +1497,17 @@ type streamableClientConn struct {
 	sessionID         string
 }
 
-// errSessionMissing distinguishes if the session is known to not be present on
-// the server (see [streamableClientConn.fail]).
+// ErrSessionMissing is a sentinel error returned by a [ClientSession] using the
+// [StreamableClientTransport], indicating the session is not present on the
+// server. This occurs when the server returns a 404 Not Found response.
 //
-// TODO(rfindley): should we expose this error value (and its corresponding
-// API) to the user?
+// According to the MCP spec ([Session Management]), clients should reestablish
+// a session when encountering this error. Users can check for this error using
+// [errors.Is] to implement session recovery logic by creating a new
+// [ClientSession].
 //
-// The spec says that if the server returns 404, clients should reestablish
-// a session. For now, we delegate that to the user, but do they need a way to
-// differentiate a 'NotFound' error from other errors?
-var errSessionMissing = errors.New("session not found")
+// [Session Management]: https://modelcontextprotocol.io/specification/2025-11-25/basic/transports#session-management
+var ErrSessionMissing = errors.New("session not found")
 
 var _ clientConnection = (*streamableClientConn)(nil)
 
@@ -1572,7 +1577,7 @@ func (c *streamableClientConn) connectStandaloneSSE() {
 // If err is non-nil, it is terminal, and subsequent (or pending) Reads will
 // fail.
 //
-// If err wraps errSessionMissing, the failure indicates that the session is no
+// If err wraps [ErrSessionMissing], the failure indicates that the session is no
 // longer present on the server, and no final DELETE will be performed when
 // closing the connection.
 func (c *streamableClientConn) fail(err error) {
@@ -1816,9 +1821,9 @@ func (c *streamableClientConn) checkResponse(requestSummary string, resp *http.R
 	// which it MUST respond to requests containing that session ID with HTTP
 	// 404 Not Found."
 	if resp.StatusCode == http.StatusNotFound {
-		// Return an errSessionMissing to avoid sending a redundant DELETE when the
+		// Return an ErrSessionMissing to avoid sending a redundant DELETE when the
 		// session is already gone.
-		return fmt.Errorf("%s: failed to connect (session ID: %v): %w", requestSummary, c.sessionID, errSessionMissing)
+		return fmt.Errorf("%s: failed to connect (session ID: %v): %w", requestSummary, c.sessionID, ErrSessionMissing)
 	}
 	if resp.StatusCode < 200 || resp.StatusCode >= 300 {
 		return fmt.Errorf("%s: failed to connect: %v", requestSummary, http.StatusText(resp.StatusCode))
@@ -1970,7 +1975,7 @@ func (c *streamableClientConn) connectSSE(ctx context.Context, lastEventID strin
 // Close implements the [Connection] interface.
 func (c *streamableClientConn) Close() error {
 	c.closeOnce.Do(func() {
-		if errors.Is(c.failure(), errSessionMissing) {
+		if errors.Is(c.failure(), ErrSessionMissing) {
 			// If the session is missing, no need to delete it.
 		} else {
 			req, err := http.NewRequestWithContext(c.ctx, http.MethodDelete, c.url, nil)
diff --git a/mcp/streamable_client.go b/mcp/streamable_client.go
index 41a10046..c2cc25b8 100644
--- a/mcp/streamable_client.go
+++ b/mcp/streamable_client.go
@@ -161,7 +161,7 @@ The client must handle two response formats from POST requests:
 
   - DELETE: Terminate the session
     - Used by [streamableClientConn.Close]
-    - Skipped if session is already known to be gone ([errSessionMissing])
+    - Skipped if session is already known to be gone ([ErrSessionMissing])
 
 # Error Handling
 
@@ -173,7 +173,7 @@ Errors are categorized and handled differently:
    - Triggers reconnection in [streamableClientConn.handleSSE]
 
 2. Terminal (breaks the connection):
-   - 404 Not Found: Session terminated by server ([errSessionMissing])
+   - 404 Not Found: Session terminated by server ([ErrSessionMissing])
    - Message decode errors: Protocol violation
    - Context cancellation: Client closed connection
    - Mismatched session IDs: Protocol error
@@ -183,7 +183,7 @@ Terminal errors are stored via [streamableClientConn.fail] and returned by
 subsequent [streamableClientConn.Read] calls. The [streamableClientConn.failed]
 channel signals that the connection is broken.
 
-Special case: [errSessionMissing] indicates the server has terminated the session,
+Special case: [ErrSessionMissing] indicates the server has terminated the session,
 so [streamableClientConn.Close] skips the DELETE request.
 
 # Protocol Version Header
diff --git a/mcp/streamable_client_test.go b/mcp/streamable_client_test.go
index dcdda322..53f61b4f 100644
--- a/mcp/streamable_client_test.go
+++ b/mcp/streamable_client_test.go
@@ -6,6 +6,7 @@ package mcp
 
 import (
 	"context"
+	"errors"
 	"fmt"
 	"io"
 	"net/http"
@@ -234,6 +235,9 @@ func TestStreamableClientRedundantDelete(t *testing.T) {
 	if err == nil {
 		t.Errorf("Listing tools: got nil error, want non-nil")
 	}
+	if !errors.Is(err, ErrSessionMissing) {
+		t.Errorf("Listing tools: got %v, want error wrapping ErrSessionMissing", err)
+	}
 	_ = session.Wait() // must not hang
 	if missing := fake.missingRequests(); len(missing) > 0 {
 		t.Errorf("did not receive expected requests: %v", missing)
diff --git a/mcp/streamable_test.go b/mcp/streamable_test.go
index 9eff74b8..e335ed10 100644
--- a/mcp/streamable_test.go
+++ b/mcp/streamable_test.go
@@ -367,6 +367,52 @@ func TestStreamableServerShutdown(t *testing.T) {
 	}
 }
 
+// TestStreamableServerSessionClose verifies that when the server closes a
+// session, the client observes ErrSessionMissing on subsequent requests.
+func TestStreamableServerSessionClose(t *testing.T) {
+	ctx := context.Background()
+
+	server := NewServer(testImpl, nil)
+	AddTool(server, &Tool{Name: "greet"}, sayHi)
+
+	handler := NewStreamableHTTPHandler(
+		func(req *http.Request) *Server { return server },
+		nil,
+	)
+
+	httpServer := httptest.NewServer(handler)
+	defer httpServer.Close()
+
+	transport := &StreamableClientTransport{Endpoint: httpServer.URL}
+	client := NewClient(testImpl, nil)
+	clientSession, err := client.Connect(ctx, transport, nil)
+	if err != nil {
+		t.Fatalf("client.Connect() failed: %v", err)
+	}
+	defer clientSession.Close()
+
+	// Verify the connection works initially.
+	if _, err := clientSession.ListTools(ctx, nil); err != nil {
+		t.Fatalf("ListTools failed: %v", err)
+	}
+
+	// Close the server session.
+	for session := range server.Sessions() {
+		if err := session.Close(); err != nil {
+			t.Fatalf("closing server session: %v", err)
+		}
+	}
+
+	// Subsequent requests should fail with ErrSessionMissing.
+	_, err = clientSession.ListTools(ctx, nil)
+	if err == nil {
+		t.Fatalf("ListTools after server session close: got nil error, want error")
+	}
+	if !errors.Is(err, ErrSessionMissing) {
+		t.Errorf("ListTools after server session close: got %v, want error wrapping ErrSessionMissing", err)
+	}
+}
+
 // TestClientReplay verifies that the client can recover from a mid-stream
 // network failure and receive replayed messages (if replay is configured). It
 // uses a proxy that is killed and restarted to simulate a recoverable network