I ended up adding a little util that catches the error and throws the custom message:

export async function expectToResolve(expected: Promise<any>, msg: string) {
  try {
    await expect(expected, "").resolves.toBeUndefined()
  } catch {
    throw new Error(msg)
  }
}

It can be used like this:

await expectToResolve(promise, "custom message");