diff --git a/Library/Homebrew/extend/os/mac/development_tools.rb b/Library/Homebrew/extend/os/mac/development_tools.rb
index f101a31056..6f25836ae3 100644
--- a/Library/Homebrew/extend/os/mac/development_tools.rb
+++ b/Library/Homebrew/extend/os/mac/development_tools.rb
@@ -51,10 +51,7 @@ class DevelopmentTools
 
     sig { returns(String) }
     def installation_instructions
-      <<~EOS
-        Install the Command Line Tools:
-          xcode-select --install
-      EOS
+      MacOS::CLT.installation_instructions
     end
 
     sig { returns(String) }
diff --git a/Library/Homebrew/extend/os/mac/diagnostic.rb b/Library/Homebrew/extend/os/mac/diagnostic.rb
index 71fe9f3c4a..69aa335b23 100644
--- a/Library/Homebrew/extend/os/mac/diagnostic.rb
+++ b/Library/Homebrew/extend/os/mac/diagnostic.rb
@@ -64,6 +64,7 @@ module Homebrew
           check_clt_minimum_version
           check_if_xcode_needs_clt_installed
           check_if_supported_sdk_available
+          check_broken_sdks
         ].freeze
       end
 
@@ -425,7 +426,7 @@ module Homebrew
 
         source = if locator.source == :clt
           update_instructions = MacOS::CLT.update_instructions
-          "CLT"
+          "Command Line Tools (CLT)"
         else
           update_instructions = MacOS::Xcode.update_instructions
           "Xcode"
@@ -438,6 +439,40 @@ module Homebrew
           #{update_instructions}
         EOS
       end
+
+      # The CLT 10.x -> 11.x upgrade process on 10.14 contained a bug which broke the SDKs.
+      # Notably, MacOSX10.14.sdk would indirectly symlink to MacOSX10.15.sdk.
+      # This diagnostic was introduced to check for this and recommend a full reinstall.
+      def check_broken_sdks
+        locator = MacOS.sdk_locator
+
+        return if locator.all_sdks.all? do |sdk|
+          path_version = sdk.path.basename.to_s[MacOS::SDK::VERSIONED_SDK_REGEX, 1]
+          next true if path_version.blank?
+
+          sdk.version == MacOS::Version.new(path_version).strip_patch
+        end
+
+        if locator.source == :clt
+          source = "Command Line Tools (CLT)"
+          path_to_remove = MacOS::CLT::PKG_PATH
+          installation_instructions = MacOS::CLT.installation_instructions
+        else
+          source = "Xcode"
+          path_to_remove = MacOS::Xcode.bundle_path
+          installation_instructions = MacOS::Xcode.installation_instructions
+        end
+
+        <<~EOS
+          The contents of the SDKs in your #{source} installation do not match the SDK folder names.
+          A clean reinstall of #{source} should fix this.
+
+          Remove the broken installation before reinstalling:
+            sudo rm -rf #{path_to_remove}
+
+          #{installation_instructions}
+        EOS
+      end
     end
   end
 end
diff --git a/Library/Homebrew/os/mac/xcode.rb b/Library/Homebrew/os/mac/xcode.rb
index 9a5f765800..7de72b63e3 100644
--- a/Library/Homebrew/os/mac/xcode.rb
+++ b/Library/Homebrew/os/mac/xcode.rb
@@ -134,6 +134,19 @@ module OS
         sdk(v)&.path
       end
 
+      def installation_instructions
+        if OS::Mac.prerelease?
+          <<~EOS
+            Xcode can be installed from:
+              #{Formatter.url("https://developer.apple.com/download/more/")}
+          EOS
+        else
+          <<~EOS
+            Xcode can be installed from the App Store.
+          EOS
+        end
+      end
+
       sig { returns(String) }
       def update_instructions
         if OS::Mac.prerelease?
@@ -254,6 +267,21 @@ module OS
         sdk(v)&.path
       end
 
+      def installation_instructions
+        if MacOS.version == "10.14"
+          # This is not available from `xcode-select`
+          <<~EOS
+            Install the Command Line Tools for Xcode 11.3.1 from:
+              #{Formatter.url("https://developer.apple.com/download/more/")}
+          EOS
+        else
+          <<~EOS
+            Install the Command Line Tools:
+              xcode-select --install
+          EOS
+        end
+      end
+
       sig { returns(String) }
       def update_instructions
         software_update_location = if MacOS.version >= "10.14"
diff --git a/Library/Homebrew/test/os/mac/diagnostic_spec.rb b/Library/Homebrew/test/os/mac/diagnostic_spec.rb
index f58aef8cff..d8c1436355 100644
--- a/Library/Homebrew/test/os/mac/diagnostic_spec.rb
+++ b/Library/Homebrew/test/os/mac/diagnostic_spec.rb
@@ -39,4 +39,79 @@ describe Homebrew::Diagnostic::Checks do
     expect(checks.check_ruby_version)
       .to match "Ruby version 1.8.6 is unsupported on 10.12"
   end
+
+  describe "#check_if_supported_sdk_available" do
+    let(:macos_version) { OS::Mac::Version.new("11") }
+
+    before do
+      allow(DevelopmentTools).to receive(:installed?).and_return(true)
+      allow(OS::Mac).to receive(:version).and_return(macos_version)
+    end
+
+    it "doesn't trigger when SDK root is not needed" do
+      allow(OS::Mac).to receive(:sdk_root_needed?).and_return(false)
+      allow(OS::Mac).to receive(:sdk).and_return(nil)
+
+      expect(checks.check_if_supported_sdk_available).to be_nil
+    end
+
+    it "doesn't trigger when a valid SDK is present" do
+      allow(OS::Mac).to receive(:sdk_root_needed?).and_return(true)
+      allow(OS::Mac).to receive(:sdk).and_return(OS::Mac::SDK.new(macos_version, "/some/path/MacOSX.sdk", :clt))
+
+      expect(checks.check_if_supported_sdk_available).to be_nil
+    end
+
+    it "triggers when a valid SDK is not present on CLT systems" do
+      allow(OS::Mac).to receive(:sdk_root_needed?).and_return(true)
+      allow(OS::Mac).to receive(:sdk).and_return(nil)
+      allow(OS::Mac).to receive(:sdk_locator).and_return(OS::Mac::CLT.sdk_locator)
+
+      expect(checks.check_if_supported_sdk_available)
+        .to include("Your Command Line Tools (CLT) does not support macOS #{macos_version}")
+    end
+
+    it "triggers when a valid SDK is not present on Xcode systems" do
+      allow(OS::Mac).to receive(:sdk_root_needed?).and_return(true)
+      allow(OS::Mac).to receive(:sdk).and_return(nil)
+      allow(OS::Mac).to receive(:sdk_locator).and_return(OS::Mac::Xcode.sdk_locator)
+
+      expect(checks.check_if_supported_sdk_available)
+        .to include("Your Xcode does not support macOS #{macos_version}")
+    end
+  end
+
+  describe "#check_broken_sdks" do
+    it "doesn't trigger when SDK versions are as expected" do
+      allow(OS::Mac).to receive(:sdk_locator).and_return(OS::Mac::CLT.sdk_locator)
+      allow_any_instance_of(OS::Mac::CLTSDKLocator).to receive(:all_sdks)
+        .and_return([
+                      OS::Mac::SDK.new(OS::Mac::Version.new("11"), "/some/path/MacOSX.sdk", :clt),
+                      OS::Mac::SDK.new(OS::Mac::Version.new("10.15"), "/some/path/MacOSX10.15.sdk", :clt),
+                    ])
+
+      expect(checks.check_broken_sdks).to be_nil
+    end
+
+    it "triggers when the CLT SDK version doesn't match the folder name" do
+      allow_any_instance_of(OS::Mac::CLTSDKLocator).to receive(:all_sdks)
+        .and_return([
+                      OS::Mac::SDK.new(OS::Mac::Version.new("10.14"), "/some/path/MacOSX10.15.sdk", :clt),
+                    ])
+
+      expect(checks.check_broken_sdks)
+        .to include("SDKs in your Command Line Tools (CLT) installation do not match the SDK folder names")
+    end
+
+    it "triggers when the Xcode SDK version doesn't match the folder name" do
+      allow(OS::Mac).to receive(:sdk_locator).and_return(OS::Mac::Xcode.sdk_locator)
+      allow_any_instance_of(OS::Mac::XcodeSDKLocator).to receive(:all_sdks)
+        .and_return([
+                      OS::Mac::SDK.new(OS::Mac::Version.new("10.14"), "/some/path/MacOSX10.15.sdk", :xcode),
+                    ])
+
+      expect(checks.check_broken_sdks)
+        .to include("The contents of the SDKs in your Xcode installation do not match the SDK folder names")
+    end
+  end
 end