diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/codegen/CodeGenerator.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/codegen/CodeGenerator.scala
index 330116e592482..75c080a85077c 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/codegen/CodeGenerator.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/codegen/CodeGenerator.scala
@@ -667,6 +667,9 @@ class CodegenContext extends Logging {
     case dt: DataType if isPrimitiveType(dt) => s"($c1 > $c2 ? 1 : $c1 < $c2 ? -1 : 0)"
     case BinaryType => s"org.apache.spark.unsafe.types.ByteArray.compareBinary($c1, $c2)"
     case CalendarIntervalType => s"$c1.compareTo($c2)"
+    // TimestampNanosVal exposes only `compareTo`; the AtomicType fallback below emits
+    // `$c1.compare($c2)`, which would not resolve as a Java method call.
+    case _: TimestampNTZNanosType | _: TimestampLTZNanosType => s"$c1.compareTo($c2)"
     case NullType => "0"
     case array: ArrayType =>
       val elementType = array.elementType
diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/types/PhysicalDataType.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/types/PhysicalDataType.scala
index d89feb7e0dfde..806ec1342c492 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/types/PhysicalDataType.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/types/PhysicalDataType.scala
@@ -177,13 +177,11 @@ case object PhysicalCalendarIntervalType extends PhysicalCalendarIntervalType
  * Storage layout is identical to [[PhysicalTimestampLTZNanosType]]; both types exist so the
  * NTZ/LTZ distinction propagates through the physical-type system to consumers that need it.
  *
- * Ordering, compare, and hash are not implemented yet and will be added in a follow-up issue.
+ * Hash is not implemented yet and will be added in a follow-up issue.
  */
 class PhysicalTimestampNTZNanosType() extends PhysicalDataType {
-  override private[sql] def ordering =
-    throw QueryExecutionErrors.orderedOperationUnsupportedByDataTypeError(
-      "PhysicalTimestampNTZNanosType")
   override private[sql] type InternalType = TimestampNanosVal
+  override private[sql] val ordering = implicitly[Ordering[InternalType]]
   @transient private[sql] lazy val tag = typeTag[InternalType]
 }
 case object PhysicalTimestampNTZNanosType extends PhysicalTimestampNTZNanosType
@@ -197,13 +195,11 @@ case object PhysicalTimestampNTZNanosType extends PhysicalTimestampNTZNanosType
  * Storage layout is identical to [[PhysicalTimestampNTZNanosType]]; both types exist so the
  * NTZ/LTZ distinction propagates through the physical-type system to consumers that need it.
  *
- * Ordering, compare, and hash are not implemented yet and will be added in a follow-up issue.
+ * Hash is not implemented yet and will be added in a follow-up issue.
  */
 class PhysicalTimestampLTZNanosType() extends PhysicalDataType {
-  override private[sql] def ordering =
-    throw QueryExecutionErrors.orderedOperationUnsupportedByDataTypeError(
-      "PhysicalTimestampLTZNanosType")
   override private[sql] type InternalType = TimestampNanosVal
+  override private[sql] val ordering = implicitly[Ordering[InternalType]]
   @transient private[sql] lazy val tag = typeTag[InternalType]
 }
 case object PhysicalTimestampLTZNanosType extends PhysicalTimestampLTZNanosType
diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/OrderingSuite.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/OrderingSuite.scala
index 06c8b5ccef652..8505a1c8a2c18 100644
--- a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/OrderingSuite.scala
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/OrderingSuite.scala
@@ -28,6 +28,7 @@ import org.apache.spark.sql.catalyst.encoders.ExpressionEncoder
 import org.apache.spark.sql.catalyst.expressions.codegen.{CodegenContext, GenerateOrdering, LazilyGeneratedOrdering}
 import org.apache.spark.sql.internal.SQLConf
 import org.apache.spark.sql.types._
+import org.apache.spark.unsafe.types.TimestampNanosVal
 import org.apache.spark.util.ArrayImplicits._
 
 class OrderingSuite extends SparkFunSuite with ExpressionEvalHelper {
@@ -141,6 +142,68 @@ class OrderingSuite extends SparkFunSuite with ExpressionEvalHelper {
     GenerateOrdering.generate(Array.fill(5000)(sortOrder).toImmutableArraySeq)
   }
 
+  // SPARK-57103: ordering for nanosecond timestamp types. Not driven by the generic
+  // `atomicTypes` loop above because `RandomDataGenerator` does not yet support the new
+  // types (tracked separately in SPARK-57034); we hand-roll edge cases here instead.
+  private def compareNanos(
+      dataType: AtomicType,
+      a: TimestampNanosVal,
+      b: TimestampNanosVal,
+      expected: Int): Unit = {
+    test(s"compare two $dataType values: a = $a, b = $b") {
+      val rowA = InternalRow(a)
+      val rowB = InternalRow(b)
+      Seq(Ascending, Descending).foreach { direction =>
+        val sortOrder = direction match {
+          case Ascending => BoundReference(0, dataType, nullable = true).asc
+          case Descending => BoundReference(0, dataType, nullable = true).desc
+        }
+        val expectedCompareResult = direction match {
+          case Ascending => signum(expected)
+          case Descending => -1 * signum(expected)
+        }
+        val intOrdering = new InterpretedOrdering(sortOrder :: Nil)
+        val genOrdering = new LazilyGeneratedOrdering(sortOrder :: Nil)
+        Seq(intOrdering, genOrdering).foreach { ordering =>
+          assert(ordering.compare(rowA, rowA) === 0)
+          assert(ordering.compare(rowB, rowB) === 0)
+          assert(signum(ordering.compare(rowA, rowB)) === expectedCompareResult)
+          assert(signum(ordering.compare(rowB, rowA)) === -1 * expectedCompareResult)
+        }
+      }
+    }
+  }
+
+  Seq(TimestampNTZNanosType(9), TimestampLTZNanosType(9)).foreach { dt =>
+    // equal values
+    compareNanos(dt,
+      TimestampNanosVal.fromParts(1000L, 100.toShort),
+      TimestampNanosVal.fromParts(1000L, 100.toShort), 0)
+    // primary key (epochMicros) decides
+    compareNanos(dt,
+      TimestampNanosVal.fromParts(1000L, 999.toShort),
+      TimestampNanosVal.fromParts(1001L, 0.toShort), -1)
+    // tie-breaker (nanosWithinMicro) within the same micro
+    compareNanos(dt,
+      TimestampNanosVal.fromParts(1000L, 100.toShort),
+      TimestampNanosVal.fromParts(1000L, 101.toShort), -1)
+    // Long boundary: plain subtraction would overflow; Ordering must use Long.compare.
+    compareNanos(dt,
+      TimestampNanosVal.fromParts(Long.MinValue, 0.toShort),
+      TimestampNanosVal.fromParts(Long.MaxValue, 0.toShort), -1)
+    // pre-epoch sorts before epoch regardless of nanos
+    compareNanos(dt,
+      TimestampNanosVal.fromParts(-1L, 999.toShort),
+      TimestampNanosVal.fromParts(0L, 0.toShort), -1)
+    // null sorts before any value under default NullsFirst semantics
+    compareNanos(dt, null, TimestampNanosVal.fromParts(0L, 0.toShort), -1)
+  }
+
+  // Ordering is precision-independent. One case at p = 7 documents that intent.
+  compareNanos(TimestampNTZNanosType(7),
+    TimestampNanosVal.fromParts(0L, 0.toShort),
+    TimestampNanosVal.fromParts(0L, 1.toShort), -1)
+
   test("SPARK-21344: BinaryType comparison does signed byte array comparison") {
     val data = Seq(
       (Array[Byte](1), Array[Byte](-1)),