diff --git a/test/http_server_http1_tests.jl b/test/http_server_http1_tests.jl
index b1d90778f..3714792e2 100644
--- a/test/http_server_http1_tests.jl
+++ b/test/http_server_http1_tests.jl
@@ -977,7 +977,18 @@ end
         response = HT._read_response(HT._ConnReader(sock), request)
         @test response.status == 200
         @test String(_read_all_server_bytes(response.body)) == "ok"
-        @test isempty(read(sock))
+        # The timeout response is best-effort. Depending on whether its write
+        # wins the race with transport shutdown, the peer observes either a
+        # clean EOF or a complete 408 response followed by EOF.
+        trailing = read(sock)
+        if !isempty(trailing)
+            timeout_io = IOBuffer(trailing)
+            timeout_response = HT._read_response(timeout_io)
+            @test timeout_response.status == 408
+            @test timeout_response.close
+            @test timeout_response.content_length == 0
+            @test eof(timeout_io)
+        end
     finally
         HT.@try_ignore begin
             NC.close(sock)
diff --git a/test/http_websocket_server_tests.jl b/test/http_websocket_server_tests.jl
index 7f2ac4f2d..9472d9084 100644
--- a/test/http_websocket_server_tests.jl
+++ b/test/http_websocket_server_tests.jl
@@ -317,45 +317,54 @@ end
 end
 
 @testset "HTTP.WebSockets server close notifies active sessions" begin
-    started = Channel{Nothing}(1)
-    finished = Channel{Nothing}(1)
-    release_handler = Channel{Nothing}(1)
-    server = W.listen!("127.0.0.1", 0) do ws
-        put!(started, nothing)
+    for secure in (false, true)
+        started = Channel{Nothing}(1)
+        finished = Channel{Nothing}(1)
+        release_handler = Channel{Nothing}(1)
+        tls_config = secure ?
+            TL.Config(verify_peer = false, cert_file = _TLS_CERT_PATH, key_file = _TLS_KEY_PATH) :
+            nothing
+        server = W.listen!("127.0.0.1", 0; tls_config = tls_config) do ws
+            put!(started, nothing)
+            try
+                while true
+                    W.receive(ws)
+                end
+            catch
+            finally
+                put!(finished, nothing)
+                take!(release_handler)
+            end
+        end
+        ws = nothing
+        forceclose_task = nothing
         try
-            while true
-                W.receive(ws)
+            address = W.server_addr(server)
+            scheme = secure ? "wss" : "ws"
+            ws = W.open(
+                "$scheme://$address/shutdown";
+                require_ssl_verification = false,
+            )
+            take!(started)
+            forceclose_task = errormonitor(Threads.@spawn W.forceclose(server))
+            take!(finished)
+            fetch(forceclose_task::Task)
+            put!(release_handler, nothing)
+            wait(server)
+            err = try
+                W.receive(ws::W.WebSocket)
+                nothing
+            catch err
+                err
             end
-        catch
+            @test err isa W.WebSocketError
+            @test (err::W.WebSocketError).message.code == 1001
         finally
-            put!(finished, nothing)
-            take!(release_handler)
+            isready(release_handler) || HTTP.@try_ignore put!(release_handler, nothing)
+            forceclose_task === nothing || HTTP.@try_ignore fetch(forceclose_task::Task)
+            ws === nothing || HTTP.@try_ignore close(ws::W.WebSocket)
+            HTTP.@try_ignore W.forceclose(server)
+            HTTP.@try_ignore wait(server)
         end
     end
-    ws = nothing
-    forceclose_task = nothing
-    try
-        address = W.server_addr(server)
-        ws = W.open("ws://$address/shutdown")
-        take!(started)
-        forceclose_task = errormonitor(Threads.@spawn W.forceclose(server))
-        take!(finished)
-        fetch(forceclose_task::Task)
-        put!(release_handler, nothing)
-        wait(server)
-        err = try
-            W.receive(ws::W.WebSocket)
-            nothing
-        catch err
-            err
-        end
-        @test err isa W.WebSocketError
-        @test (err::W.WebSocketError).message.code == 1001
-    finally
-        isready(release_handler) || HTTP.@try_ignore put!(release_handler, nothing)
-        forceclose_task === nothing || HTTP.@try_ignore fetch(forceclose_task::Task)
-        ws === nothing || HTTP.@try_ignore close(ws::W.WebSocket)
-        HTTP.@try_ignore W.forceclose(server)
-        HTTP.@try_ignore wait(server)
-    end
 end