diff --git a/conan/cps/cps.py b/conan/cps/cps.py
index 6e04b7b8bbb..f4dbe944f8c 100644
--- a/conan/cps/cps.py
+++ b/conan/cps/cps.py
@@ -40,6 +40,7 @@ def __init__(self, component_type=None):
         self.requires = []
         self.location = None
         self.link_location = None
+        self.link_languages = None
         self.link_libraries = None  # system libraries
 
     def serialize(self):
@@ -56,6 +57,8 @@ def serialize(self):
             component["link_location"] = self.link_location
         if self.link_libraries:
             component["link_libraries"] = self.link_libraries
+        if self.link_languages:
+            component["link_languages"] = self.link_languages
         return component
 
     @staticmethod
@@ -68,6 +71,7 @@ def deserialize(data):
         comp.location = data.get("location")
         comp.link_location = data.get("link_location")
         comp.link_libraries = data.get("link_libraries")
+        comp.link_languages = data.get("link_languages")
         return comp
 
     @staticmethod
@@ -90,12 +94,15 @@ def from_cpp_info(cpp_info, conanfile, libname=None):
         cps_comp.location = cpp_info.location
         cps_comp.link_location = cpp_info.link_location
         cps_comp.link_libraries = cpp_info.system_libs
+        langs = {"C": "c", "C++": "cpp"}
+        cps_comp.link_languages = [langs[lang] for lang in cpp_info.languages or []]
         required = cpp_info.requires
         cps_comp.requires = [f":{c}" if "::" not in c else c.replace("::", ":") for c in required]
         return cps_comp
 
     def update(self, conf, conf_def):
         # TODO: conf not used at the moent
+        self.link_languages = self.link_languages or conf_def.get("link_languages")
         self.location = self.location or conf_def.get("location")
         self.link_location = self.link_location or conf_def.get("link_location")
         self.link_libraries = self.link_libraries or conf_def.get("link_libraries")
@@ -223,6 +230,29 @@ def strip_prefix(dirs):
                     basefile = basefile[3:]
                 cpp_info.libs = [basefile]
                 # FIXME: Missing requires
+            elif comp.type is CPSComponentType.DYLIB:
+                if comp.link_location:
+                    link_location = comp.link_location
+                    link_location = link_location.replace("@prefix@/", "")
+                    cpp_info.libdirs = [os.path.dirname(link_location)]
+                    filename = os.path.basename(link_location)
+                    basefile, ext = os.path.splitext(filename)
+                    if basefile.startswith("lib") and ext != ".lib":
+                        basefile = basefile[3:]
+                    cpp_info.libs = [basefile]
+                    location = comp.location
+                    location = location.replace("@prefix@/", "")
+                    cpp_info.bindirs = [os.path.dirname(location)]
+                else:  # TODO: same as archive, refactor
+                    location = comp.location
+                    location = location.replace("@prefix@/", "")
+                    cpp_info.libdirs = [os.path.dirname(location)]
+                    filename = os.path.basename(location)
+                    basefile, ext = os.path.splitext(filename)
+                    if basefile.startswith("lib") and ext != ".lib":
+                        basefile = basefile[3:]
+                    cpp_info.libs = [basefile]
+                    # FIXME: Missing requires
             cpp_info.system_libs = comp.link_libraries
         else:
             for comp_name, comp in self.components.items():
diff --git a/conan/tools/cmake/cmakedeps2/cmakedeps.py b/conan/tools/cmake/cmakedeps2/cmakedeps.py
index e2ab0b6e657..34893a35ddf 100644
--- a/conan/tools/cmake/cmakedeps2/cmakedeps.py
+++ b/conan/tools/cmake/cmakedeps2/cmakedeps.py
@@ -259,7 +259,8 @@ def generate(self):
             pkg_name = self._cmakedeps.get_cmake_filename(dep)
             # https://cmake.org/cmake/help/v3.22/guide/using-dependencies/index.html
             if cmake_find_mode == FIND_MODE_NONE:
-                cps = glob.glob(f"**/{pkg_name}.cps", root_dir=dep.package_folder, recursive=True)
+                cps = glob.glob(os.path.join(dep.package_folder, f"**/{pkg_name}.cps"),
+                                recursive=True)
                 if cps:
                     loc = os.path.dirname(os.path.join(dep.package_folder, cps[0]))
                     loc = loc.replace("\\", "/")
diff --git a/test/functional/toolchains/cmake/test_cps.py b/test/functional/toolchains/cmake/test_cps.py
index ad660a40eca..222747e3df9 100644
--- a/test/functional/toolchains/cmake/test_cps.py
+++ b/test/functional/toolchains/cmake/test_cps.py
@@ -8,7 +8,8 @@
 
 
 @pytest.mark.tool("cmake", "4.2")
-def test_cps():
+@pytest.mark.parametrize("shared", [False, True])
+def test_cps(shared):
     c = TestClient()
     c.run("new cmake_lib")
     conanfile = textwrap.dedent("""\
@@ -67,7 +68,9 @@ def package_info(self):
     # First, try with the standard mypkg-config.cmake consumption
     c.save({"conanfile.py": conanfile,
             "CMakeLists.txt": cmake})
-    c.run("create")
+
+    shared_arg = "-o &:shared=True" if shared else ""
+    c.run(f"create {shared_arg}")
     assert "mypkg/0.1: Hello World Release!" in c.out
 
     # Lets consume directly with CPS
@@ -119,5 +122,5 @@ def test(self):
     shutil.rmtree(os.path.join(c.current_folder, "test_package", "build"))
     c.save({"test_package/conanfile.py": test_conanfile,
             "test_package/CMakeLists.txt": test_cmake})
-    c.run("create --build=missing -c tools.cmake.cmakedeps:new=will_break_next")
+    c.run(f"create {shared_arg} --build=never -c tools.cmake.cmakedeps:new=will_break_next")
     assert "mypkg/0.1: Hello World Release!" in c.out
diff --git a/test/integration/cps/test_cps.py b/test/integration/cps/test_cps.py
index 407f91a13ba..6dfbcee5338 100644
--- a/test/integration/cps/test_cps.py
+++ b/test/integration/cps/test_cps.py
@@ -122,38 +122,106 @@ def package_info(self):
     assert 'set(zlib_LIBS_RELEASE zlib)' in cmake
 
 
-def test_cps_merge():
-    folder = temp_folder()
-    cps_base = textwrap.dedent("""
+def test_cps_shared_in_pkg():
+    c = TestClient()
+    cps = textwrap.dedent("""\
         {
-          "components" : {
-            "mypkg" : {
+          "components" :
+          {
+            "mypkg" :
+            {
               "includes" : [ "@prefix@/include" ],
-              "type" : "archive"
+              "type" : "dylib"
             }
           },
-          "cps_version" : "0.12.0",
-          "name" : "mypkg",
-          "version" : "1.0"
+          "cps_path" : "@prefix@/cps",
+          "cps_version" : "0.13.0",
+          "name" : "mypkg"
         }
         """)
-    cps_conf = textwrap.dedent("""
+    cps_release = textwrap.dedent("""\
         {
-          "components" : {
-            "mypkg" : {
-              "link_languages" : [ "cpp" ],
-              "location" : "@prefix@/lib/mypkg.lib"
+          "components" :
+          {
+            "mypkg" :
+            {
+              "link_location" : "@prefix@/lib/mypkg.lib",
+              "location" : "@prefix@/bin/mypkg.dll"
             }
           },
           "configuration" : "Release",
           "name" : "mypkg"
         }
         """)
+    cps = "".join(cps.splitlines())
+    cps_release = "".join(cps_release.splitlines())
+    conanfile = textwrap.dedent(f"""
+        import os, json
+        from conan.tools.files import save
+        from conan import ConanFile
+        class Pkg(ConanFile):
+            name = "mypkg"
+            version = "1.0"
+
+            def package(self):
+                cps = '{cps}'
+                cps_path = os.path.join(self.package_folder, "mypkg.cps")
+                save(self, cps_path, cps)
+                cps = '{cps_release}'
+                cps_path = os.path.join(self.package_folder, "mypkg@release.cps")
+                save(self, cps_path, cps)
+
+            def package_info(self):
+                from conan.cps import CPS
+                self.cpp_info = CPS.load("mypkg.cps").to_conan()
+        """)
+    c.save({"pkg/conanfile.py": conanfile})
+    c.run("create pkg")
+
+    settings = "-s os=Windows -s compiler=msvc -s compiler.version=191 -s arch=x86_64"
+
+    c.run(f"install --requires=mypkg/1.0 {settings} -g CMakeDeps")
+    cmake = c.load("mypkg-release-x86_64-data.cmake")
+    assert 'set(mypkg_INCLUDE_DIRS_RELEASE "${mypkg_PACKAGE_FOLDER_RELEASE}/include")' in cmake
+    assert 'set(mypkg_LIB_DIRS_RELEASE "${mypkg_PACKAGE_FOLDER_RELEASE}/lib")'
+    assert 'set(mypkg_LIBS_RELEASE mypkg)' in cmake
+
+
+def test_cps_merge():
+    folder = temp_folder()
+
+    cps_base = textwrap.dedent("""{
+        "components": {
+            "mypkg":{
+                "includes": ["@prefix@/include"],
+                "type": "archive"
+            }
+        },
+        "cps_path": "@prefix@/cps",
+        "cps_version": "0.13.0",
+        "name": "mypkg"
+        }
+        """)
+    cps_conf = textwrap.dedent("""{
+        "components" : {
+            "mypkg" : {
+                "link_languages" : [ "cpp" ],
+                "location" : "@prefix@/lib/mypkg.lib"
+            }
+        },
+        "configuration" : "Release",
+        "name" : "mypkg"
+        }
+        """)
     save_files(folder, {"mypkg.cps": cps_base,
                         "mypkg@release.cps": cps_conf})
     cps = CPS.load(os.path.join(folder, "mypkg.cps"))
     json_cps = cps.serialize()
-    print(json.dumps(json_cps, indent=2))
+    mypkg = json_cps["components"]["mypkg"]
+    assert mypkg["includes"] == ["@prefix@/include"]
+    assert mypkg["location"] == "@prefix@/lib/mypkg.lib"
+    assert mypkg["type"] == "archive"
+    assert mypkg["link_languages"] == ["cpp"]
 
 
 def test_extended_cpp_info():