diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index e5b2ffc..c42c813 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -4,15 +4,18 @@ on: [push, pull_request]
 jobs:
   test:
     name: Test
-    runs-on: ubuntu-latest
+    runs-on: ${{ matrix.os }}
     strategy:
       matrix:
+        os: [ubuntu-latest, macos-latest, windows-latest]
         rust: [stable, beta, nightly]
     steps:
     - uses: actions/checkout@master
     - name: Install Rust
       run: rustup update ${{ matrix.rust }} && rustup default ${{ matrix.rust }}
     - run: cargo test
+    - name: Integration test
+      run: cargo test --manifest-path test-crate/Cargo.toml
 
   rustfmt:
     name: Rustfmt
@@ -40,3 +43,67 @@ jobs:
           git -c user.name='ci' -c user.email='ci' commit -m init
           git push -f -q https://git:${{ secrets.github_token }}@github.com/${{ github.repository }} HEAD:gh-pages
         if: github.event_name == 'push' && github.event.ref == 'refs/heads/master'
+
+  cross_compile_test:
+    name: Test Cross Compile - ${{ matrix.platform.target }}
+    needs: [ test ]
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        platform:
+          # Testable
+          - target: aarch64-unknown-linux-gnu
+            test: true
+          - target: arm-unknown-linux-gnueabihf
+            test: true
+          - target: armv7-unknown-linux-gnueabihf
+            test: true
+          - target: mips-unknown-linux-gnu
+            test: true
+          - target: mips64-unknown-linux-gnuabi64
+            test: true
+          - target: mips64el-unknown-linux-gnuabi64
+            test: true
+          - target: mipsel-unknown-linux-gnu
+            test: true
+          - target: powerpc-unknown-linux-gnu
+            test: true
+          - target: powerpc64-unknown-linux-gnu
+            test: true
+          - target: powerpc64le-unknown-linux-gnu
+            test: true
+          - target: s390x-unknown-linux-gnu
+            test: true
+          - target: x86_64-unknown-linux-musl
+            test: true
+          - target: aarch64-unknown-linux-musl
+            test: true
+          - target: x86_64-pc-windows-gnu
+            test: true
+          # Build only
+          - target: x86_64-unknown-freebsd
+            test: false
+          - target: x86_64-unknown-netbsd
+            test: false
+          - target: x86_64-sun-solaris
+            test: false
+          - target: x86_64-unknown-illumos
+            test: false
+    steps:
+    - uses: actions/checkout@master
+    - uses: actions-rs/toolchain@v1
+      with:
+        toolchain: stable
+        target: ${{ matrix.platform.target }}
+    - uses: taiki-e/install-action@v1
+      with:
+        tool: cross
+    - name: cross test
+      run: cross test -vv --target ${{ matrix.platform.target }}
+      working-directory: test-crate
+      if: ${{ matrix.platform.test }}
+    - name: cross build
+      run: cross build -vv --target ${{ matrix.platform.target }}
+      working-directory: test-crate
+      if: ${{ !matrix.platform.test }}
diff --git a/src/lib.rs b/src/lib.rs
index 3c6bfd9..63297c9 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -443,6 +443,55 @@ impl Config {
         if !self.defined("CMAKE_TOOLCHAIN_FILE") {
             if let Some(s) = self.getenv_target_os("CMAKE_TOOLCHAIN_FILE") {
                 self.define("CMAKE_TOOLCHAIN_FILE", s);
+            } else {
+                if target.contains("redox") {
+                    if !self.defined("CMAKE_SYSTEM_NAME") {
+                        self.define("CMAKE_SYSTEM_NAME", "Generic");
+                    }
+                } else if target != host && !self.defined("CMAKE_SYSTEM_NAME") {
+                    // Set CMAKE_SYSTEM_NAME and CMAKE_SYSTEM_PROCESSOR when cross compiling
+                    let os = getenv_unwrap("CARGO_CFG_TARGET_OS");
+                    let arch = getenv_unwrap("CARGO_CFG_TARGET_ARCH");
+                    // CMAKE_SYSTEM_NAME list
+                    // https://gitlab.kitware.com/cmake/cmake/-/issues/21489#note_1077167
+                    //
+                    // CMAKE_SYSTEM_PROCESSOR
+                    // some of the values come from https://en.wikipedia.org/wiki/Uname
+                    let (system_name, system_processor) = match (os.as_str(), arch.as_str()) {
+                        ("android", arch) => ("Android", arch),
+                        ("dragonfly", arch) => ("DragonFly", arch),
+                        ("macos", "x86_64") => ("Darwin", "x86_64"),
+                        ("macos", "aarch64") => ("Darwin", "arm64"),
+                        ("freebsd", "x86_64") => ("FreeBSD", "amd64"),
+                        ("freebsd", arch) => ("FreeBSD", arch),
+                        ("fuchsia", arch) => ("Fuchsia", arch),
+                        ("haiku", arch) => ("Haiku", arch),
+                        ("ios", "aarch64") => ("iOS", "arm64"),
+                        ("ios", arch) => ("iOS", arch),
+                        ("linux", arch) => {
+                            let name = "Linux";
+                            match arch {
+                                "powerpc" => (name, "ppc"),
+                                "powerpc64" => (name, "ppc64"),
+                                "powerpc64le" => (name, "ppc64le"),
+                                _ => (name, arch),
+                            }
+                        }
+                        ("netbsd", arch) => ("NetBSD", arch),
+                        ("openbsd", "x86_64") => ("OpenBSD", "amd64"),
+                        ("openbsd", arch) => ("OpenBSD", arch),
+                        ("solaris", arch) => ("SunOS", arch),
+                        ("tvos", arch) => ("tvOS", arch),
+                        ("watchos", arch) => ("watchOS", arch),
+                        ("windows", "x86_64") => ("Windows", "AMD64"),
+                        ("windows", "i686") => ("Windows", "X86"),
+                        ("windows", "aarch64") => ("Windows", "ARM64"),
+                        // Others
+                        (os, arch) => (os, arch),
+                    };
+                    self.define("CMAKE_SYSTEM_NAME", system_name);
+                    self.define("CMAKE_SYSTEM_PROCESSOR", system_processor);
+                }
             }
         }
 
@@ -561,9 +610,6 @@ impl Config {
                 // variables which will hopefully get things to succeed. Some
                 // systems may need the `windres` or `dlltool` variables set, so
                 // set them if possible.
-                if !self.defined("CMAKE_SYSTEM_NAME") {
-                    cmd.arg("-DCMAKE_SYSTEM_NAME=Windows");
-                }
                 if !self.defined("CMAKE_RC_COMPILER") {
                     let exe = find_exe(c_compiler.path());
                     if let Some(name) = exe.file_name().unwrap().to_str() {
@@ -614,14 +660,6 @@ impl Config {
                     panic!("unsupported msvc target: {}", target);
                 }
             }
-        } else if target.contains("redox") {
-            if !self.defined("CMAKE_SYSTEM_NAME") {
-                cmd.arg("-DCMAKE_SYSTEM_NAME=Generic");
-            }
-        } else if target.contains("solaris") {
-            if !self.defined("CMAKE_SYSTEM_NAME") {
-                cmd.arg("-DCMAKE_SYSTEM_NAME=SunOS");
-            }
         } else if target.contains("apple-ios") || target.contains("apple-tvos") {
             // These two flags prevent CMake from adding an OSX sysroot, which messes up compilation.
             if !self.defined("CMAKE_OSX_SYSROOT") && !self.defined("CMAKE_OSX_DEPLOYMENT_TARGET") {
diff --git a/test-crate/.gitignore b/test-crate/.gitignore
new file mode 100644
index 0000000..4fffb2f
--- /dev/null
+++ b/test-crate/.gitignore
@@ -0,0 +1,2 @@
+/target
+/Cargo.lock
diff --git a/test-crate/Cargo.toml b/test-crate/Cargo.toml
new file mode 100644
index 0000000..f3900ad
--- /dev/null
+++ b/test-crate/Cargo.toml
@@ -0,0 +1,12 @@
+[package]
+name = "test-crate"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+libz-sys = { version = "1.1.8", default-features = false, features = ["zlib-ng"] }
+
+[patch.crates-io]
+cmake = { path = ".." }
diff --git a/test-crate/src/lib.rs b/test-crate/src/lib.rs
new file mode 100644
index 0000000..036604f
--- /dev/null
+++ b/test-crate/src/lib.rs
@@ -0,0 +1,13 @@
+#[cfg(test)]
+mod tests {
+    use libz_sys::zlibVersion;
+    use std::ffi::CStr;
+
+    #[test]
+    fn zlib_version() {
+        let ver = unsafe { zlibVersion() };
+        let ver_cstr = unsafe { CStr::from_ptr(ver) };
+        let version = ver_cstr.to_str().unwrap();
+        assert!(!version.is_empty());
+    }
+}