diff --git a/src/cuda/api/context.hpp b/src/cuda/api/context.hpp
index f1381f16..8bf91e77 100644
--- a/src/cuda/api/context.hpp
+++ b/src/cuda/api/context.hpp
@@ -759,14 +759,16 @@ class context_t {
 
 /// @note: The comparison ignores whether or not the wrapper is owning
 ///@{
-inline bool operator==(const context_t& lhs, const context_t& rhs)
+inline bool operator==(const context_t& lhs, const context_t& rhs) noexcept
 {
-	return lhs.handle() == rhs.handle();
+	// Note: Contexts on different devices cannot have the same context handle,
+	// so this is redundant, but let's be extra safe:
+	return lhs.device_id() == rhs.device_id() and lhs.handle() == rhs.handle();
 }
 
-inline bool operator!=(const context_t& lhs, const context_t& rhs)
+inline bool operator!=(const context_t& lhs, const context_t& rhs) noexcept
 {
-	return lhs.handle() != rhs.handle();
+	return not (lhs == rhs);
 }
 ///@}
 
diff --git a/src/cuda/api/kernel.hpp b/src/cuda/api/kernel.hpp
index d974a6be..5575cce5 100644
--- a/src/cuda/api/kernel.hpp
+++ b/src/cuda/api/kernel.hpp
@@ -587,6 +587,19 @@ inline grid::dimension_t kernel_t::max_active_blocks_per_multiprocessor(
 		dynamic_shared_memory_per_block, disable_caching_override);
 }
 
+inline bool operator==(const kernel_t& lhs, const kernel_t& rhs) noexcept
+{
+	return
+		    lhs.device_id()      == rhs.device_id()
+		and lhs.context_handle() == rhs.context_handle()
+		and lhs.handle()         == rhs.handle();
+}
+
+inline bool operator!=(const kernel_t& lhs, const kernel_t& rhs) noexcept
+{
+	return not (lhs == rhs);
+}
+
 } // namespace cuda
 
 #endif // CUDA_API_WRAPPERS_KERNEL_HPP_