diff --git a/src/Encoder.ts b/src/Encoder.ts
index b047c1d..76051fe 100644
--- a/src/Encoder.ts
+++ b/src/Encoder.ts
@@ -72,6 +72,10 @@ export type EncoderOptions<ContextType = undefined> = Partial<
 > &
   ContextOf<ContextType>;
 
+// Bounds of the int64/uint64 range msgpack can represent, precomputed once for encodeBigInt64.
+const INT64_MIN = -(BigInt(2) ** BigInt(63));
+const UINT64_MAX = BigInt(2) ** BigInt(64) - BigInt(1);
+
 export class Encoder<ContextType = undefined> {
   private readonly extensionCodec: ExtensionCodecType<ContextType>;
   private readonly context: ContextType;
@@ -291,6 +295,9 @@ export class Encoder<ContextType = undefined> {
   }
 
   private encodeBigInt64(object: bigint): void {
+    if (object < INT64_MIN || object > UINT64_MAX) {
+      throw new Error(`Cannot encode BigInt as int64/uint64 because it is out of range: ${object}`);
+    }
     if (object >= BigInt(0)) {
       // uint 64
       this.writeU8(0xcf);
diff --git a/test/bigint64.test.ts b/test/bigint64.test.ts
index e2bf08f..f6f5c96 100644
--- a/test/bigint64.test.ts
+++ b/test/bigint64.test.ts
@@ -35,4 +35,30 @@ describe("useBigInt64: true", () => {
     const encoded = encode(value, { useBigInt64: true });
     assert.deepStrictEqual(decode(encoded, { useBigInt64: true }), value);
   });
+
+  it("round-trips the boundary values of int64/uint64", () => {
+    const values = [
+      BigInt(0),
+      BigInt(42),
+      BigInt(2) ** BigInt(63) - BigInt(1), // max int64
+      -(BigInt(2) ** BigInt(63)), // min int64
+      BigInt(2) ** BigInt(64) - BigInt(1), // max uint64
+    ];
+    for (const value of values) {
+      const encoded = encode(value, { useBigInt64: true });
+      assert.deepStrictEqual(decode(encoded, { useBigInt64: true }), value);
+    }
+  });
+
+  it("throws when a bigint is out of the int64/uint64 range", () => {
+    const values = [
+      BigInt(2) ** BigInt(64), // uint64 max + 1
+      BigInt(2) ** BigInt(64) + BigInt(1),
+      -(BigInt(2) ** BigInt(63)) - BigInt(1), // int64 min - 1
+      -(BigInt(2) ** BigInt(100)),
+    ];
+    for (const value of values) {
+      assert.throws(() => encode(value, { useBigInt64: true }), /out of range/);
+    }
+  });
 });