diff --git a/lib/postgrex/extensions/timestamptz.ex b/lib/postgrex/extensions/timestamptz.ex
index acd2d89c..888e5bdb 100644
--- a/lib/postgrex/extensions/timestamptz.ex
+++ b/lib/postgrex/extensions/timestamptz.ex
@@ -37,8 +37,19 @@ defmodule Postgrex.Extensions.TimestampTZ do
   ## Helpers
 
   def encode_elixir(%DateTime{utc_offset: 0, std_offset: 0} = datetime) do
-    microsecs = DateTime.to_unix(datetime, :microsecond)
-    <<8::int32(), microsecs - @us_epoch::int64()>>
+    microsecs = DateTime.to_unix(datetime, :microsecond) - @us_epoch
+
+    # PostgreSQL rejects timestamps outside its own range, but only when it
+    # receives the value we meant to send. Anything that does not fit in a
+    # signed 64-bit integer is silently truncated by the binary construction
+    # below and arrives as a different, in-range timestamp; the two endpoints
+    # are the infinity sentinels.
+    if microsecs > @minus_infinity and microsecs < @plus_infinity do
+      <<8::int32(), microsecs::int64()>>
+    else
+      raise ArgumentError,
+            "#{inspect(datetime)} is beyond the range PostgreSQL can represent in a timestamptz"
+    end
   end
 
   def encode_elixir(%DateTime{} = datetime) do
diff --git a/test/calendar_test.exs b/test/calendar_test.exs
index 36c0df6a..16db094c 100644
--- a/test/calendar_test.exs
+++ b/test/calendar_test.exs
@@ -299,6 +299,27 @@ defmodule CalendarTest do
     assert message =~ "timestamp out of range"
   end
 
+  if Version.match?(System.version(), ">= 1.19.0") do
+    test "encode timestamptz beyond the 64-bit wire range", context do
+      # These do not fit in the signed 64-bit microsecond wire format. Truncating
+      # them sends PostgreSQL a different, in-range timestamp that it accepts, so
+      # the value has to be rejected here instead.
+      sentinel =
+        DateTime.from_naive!(NaiveDateTime.new!(294_277, 1, 9, 4, 0, 54, {775_807, 6}), "Etc/UTC")
+
+      wraps_into_range =
+        DateTime.from_naive!(NaiveDateTime.new!(585_706, 1, 1, 0, 0, 0), "Etc/UTC")
+
+      assert_raise ArgumentError, ~r/beyond the range/, fn ->
+        query("SELECT $1::timestamptz", [sentinel])
+      end
+
+      assert_raise ArgumentError, ~r/beyond the range/, fn ->
+        query("SELECT $1::timestamptz", [wraps_into_range])
+      end
+    end
+  end
+
   @tag :capture_log
   test "decode infinity", context do
     assert_raise ArgumentError, fn -> query("SELECT 'infinity'::timestamp", []) end