diff --git a/__tests__/download/download-version.test.ts b/__tests__/download/download-version.test.ts
index b2352dc..25c02d3 100644
--- a/__tests__/download/download-version.test.ts
+++ b/__tests__/download/download-version.test.ts
@@ -146,6 +146,28 @@ describe("download-version", () => {
       expect(mockGetAllVersions).not.toHaveBeenCalled();
     });
 
+    it("resolves ~= with PEP 440 compatible release semantics", async () => {
+      mockGetFirstMatchingVersion.mockImplementation(
+        (predicate: (version: string) => boolean) =>
+          ["1.0.0", "0.10.2", "0.9.26"].find(predicate),
+      );
+
+      const version = await resolveVersion("~=0.9", undefined);
+
+      expect(version).toBe("0.10.2");
+    });
+
+    it("resolves ~= with PEP 440 compatible release semantics from manifest-file", async () => {
+      mockGetAllVersions.mockResolvedValue(["1.0.0", "0.10.2", "0.9.26"]);
+
+      const version = await resolveVersion(
+        "~=0.9",
+        "https://example.com/custom.ndjson",
+      );
+
+      expect(version).toBe("0.10.2");
+    });
+
     it("treats == exact pins as explicit versions", async () => {
       const version = await resolveVersion("==0.9.26", undefined);
 
diff --git a/dist/setup/index.cjs b/dist/setup/index.cjs
index b76c0c6..0b7cf0c 100644
--- a/dist/setup/index.cjs
+++ b/dist/setup/index.cjs
@@ -101937,7 +101937,7 @@ async function resolveVersion(versionInput, manifestUrl, resolutionStrategy = "h
   throw new Error(`No version found for ${versionInput}`);
 }
 async function findHighestSatisfyingVersion(versionSpecifier) {
-  const semverRange = semver5.validRange(versionSpecifier);
+  const semverRange = isCompatibleReleaseSpecifier(versionSpecifier) ? null : semver5.validRange(versionSpecifier);
   if (semverRange !== null) {
     const semverMatch = await getFirstMatchingVersion(
       (version3) => semver5.satisfies(version3, semverRange)
@@ -101959,8 +101959,11 @@ async function findHighestSatisfyingVersion(versionSpecifier) {
   }
   return pep440Match;
 }
+function isCompatibleReleaseSpecifier(versionSpecifier) {
+  return versionSpecifier.includes("~=");
+}
 function maxSatisfying2(versions, version3) {
-  const maxSemver = evaluateVersions(versions, version3);
+  const maxSemver = isCompatibleReleaseSpecifier(version3) ? "" : evaluateVersions(versions, version3);
   if (maxSemver !== "") {
     debug(`Found a version that satisfies the semver range: ${maxSemver}`);
     return maxSemver;
@@ -101975,7 +101978,7 @@ function maxSatisfying2(versions, version3) {
   return void 0;
 }
 function minSatisfying3(versions, version3) {
-  const minSemver = semver5.minSatisfying(versions, version3);
+  const minSemver = isCompatibleReleaseSpecifier(version3) ? null : semver5.minSatisfying(versions, version3);
   if (minSemver !== null) {
     debug(`Found a version that satisfies the semver range: ${minSemver}`);
     return minSemver;
diff --git a/src/version/resolve.ts b/src/version/resolve.ts
index ea54af7..1153c9d 100644
--- a/src/version/resolve.ts
+++ b/src/version/resolve.ts
@@ -169,7 +169,9 @@ async function findHighestSatisfyingVersion(
 ): Promise<string | undefined> {
   // This fast path assumes uv releases are semver-monotonic: newer manifest
   // entries always have higher versions, with no lower-version backports.
-  const semverRange = semver.validRange(versionSpecifier);
+  const semverRange = isCompatibleReleaseSpecifier(versionSpecifier)
+    ? null
+    : semver.validRange(versionSpecifier);
   if (semverRange !== null) {
     const semverMatch = await getFirstMatchingVersion((version) =>
       semver.satisfies(version, semverRange),
@@ -193,11 +195,20 @@ async function findHighestSatisfyingVersion(
   return pep440Match;
 }
 
+// `~=` is the PEP 440 compatible release operator. semver accepts it as a
+// tilde range with a narrower upper bound (`~=0.5` as `<0.6.0` instead of
+// `<1.0`), so it must only be evaluated as PEP 440.
+function isCompatibleReleaseSpecifier(versionSpecifier: string): boolean {
+  return versionSpecifier.includes("~=");
+}
+
 function maxSatisfying(
   versions: string[],
   version: string,
 ): string | undefined {
-  const maxSemver = tc.evaluateVersions(versions, version);
+  const maxSemver = isCompatibleReleaseSpecifier(version)
+    ? ""
+    : tc.evaluateVersions(versions, version);
   if (maxSemver !== "") {
     core.debug(`Found a version that satisfies the semver range: ${maxSemver}`);
     return maxSemver;
@@ -218,7 +229,9 @@ function minSatisfying(
   versions: string[],
   version: string,
 ): string | undefined {
-  const minSemver = semver.minSatisfying(versions, version);
+  const minSemver = isCompatibleReleaseSpecifier(version)
+    ? null
+    : semver.minSatisfying(versions, version);
   if (minSemver !== null) {
     core.debug(`Found a version that satisfies the semver range: ${minSemver}`);
     return minSemver;