diff --git a/clang-tools-extra/clang-tidy/bugprone/BranchCloneCheck.cpp b/clang-tools-extra/clang-tidy/bugprone/BranchCloneCheck.cpp
--- a/clang-tools-extra/clang-tidy/bugprone/BranchCloneCheck.cpp
+++ b/clang-tools-extra/clang-tidy/bugprone/BranchCloneCheck.cpp
@@ -59,7 +59,8 @@
 
 void BranchCloneCheck::registerMatchers(MatchFinder *Finder) {
   Finder->addMatcher(
-      ifStmt(stmt().bind("if"),
+      ifStmt(unless(allOf(isConstexpr(), isInTemplateInstantiation())),
+             stmt().bind("if"),
              hasParent(stmt(unless(ifStmt(hasElse(equalsBoundNode("if")))))),
              hasElse(stmt().bind("else"))),
       this);
diff --git a/clang-tools-extra/clang-tidy/readability/BracesAroundStatementsCheck.cpp b/clang-tools-extra/clang-tidy/readability/BracesAroundStatementsCheck.cpp
--- a/clang-tools-extra/clang-tidy/readability/BracesAroundStatementsCheck.cpp
+++ b/clang-tools-extra/clang-tidy/readability/BracesAroundStatementsCheck.cpp
@@ -123,7 +123,10 @@
 }
 
 void BracesAroundStatementsCheck::registerMatchers(MatchFinder *Finder) {
-  Finder->addMatcher(ifStmt().bind("if"), this);
+  Finder->addMatcher(
+      ifStmt(unless(allOf(isConstexpr(), isInTemplateInstantiation())))
+          .bind("if"),
+      this);
   Finder->addMatcher(whileStmt().bind("while"), this);
   Finder->addMatcher(doStmt().bind("do"), this);
   Finder->addMatcher(forStmt().bind("for"), this);
diff --git a/clang-tools-extra/test/clang-tidy/checkers/bugprone-branch-clone-if-constexpr-template.cpp b/clang-tools-extra/test/clang-tidy/checkers/bugprone-branch-clone-if-constexpr-template.cpp
new file mode 100644
--- /dev/null
+++ b/clang-tools-extra/test/clang-tidy/checkers/bugprone-branch-clone-if-constexpr-template.cpp
@@ -0,0 +1,58 @@
+// RUN: %check_clang_tidy %s bugprone-branch-clone %t -- -- -std=c++17
+
+void handle(int);
+
+template <unsigned Index>
+void shouldFail() {
+  if constexpr (Index == 0) {
+    // CHECK-MESSAGES: :[[@LINE-1]]:29: warning: repeated branch in conditional chain [bugprone-branch-clone]
+    handle(0);
+  } else if constexpr (Index == 1) {
+    handle(1);
+  } else {
+    handle(0);
+  }
+}
+
+template <unsigned Index>
+void shouldPass() {
+  if constexpr (Index == 0) {
+    handle(0);
+  } else if constexpr (Index == 1) {
+    handle(1);
+  } else {
+    handle(2);
+  }
+}
+
+void shouldFailNonTemplate() {
+  constexpr unsigned Index = 1;
+  if constexpr (Index == 0) {
+    // CHECK-MESSAGES: :[[@LINE-1]]:29: warning: repeated branch in conditional chain [bugprone-branch-clone]
+    handle(0);
+  } else if constexpr (Index == 1) {
+    handle(1);
+  } else {
+    handle(0);
+  }
+}
+
+void shouldPassNonTemplate() {
+  constexpr unsigned Index = 1;
+  if constexpr (Index == 0) {
+    handle(0);
+  } else if constexpr (Index == 1) {
+    handle(1);
+  } else {
+    handle(2);
+  }
+}
+
+void run() {
+    shouldFail<0>();
+    shouldFail<1>();
+    shouldFail<2>();
+    shouldPass<0>();
+    shouldPass<1>();
+    shouldPass<2>();
+}
diff --git a/clang-tools-extra/test/clang-tidy/checkers/readability-braces-around-statements-constexpr-if-templates.cpp b/clang-tools-extra/test/clang-tidy/checkers/readability-braces-around-statements-constexpr-if-templates.cpp
new file mode 100644
--- /dev/null
+++ b/clang-tools-extra/test/clang-tidy/checkers/readability-braces-around-statements-constexpr-if-templates.cpp
@@ -0,0 +1,48 @@
+// RUN: %check_clang_tidy %s readability-braces-around-statements %t -- -- -std=c++17
+
+void handle(bool);
+
+template <bool branch>
+void shouldFail() {
+  if constexpr (branch)
+  // CHECK-MESSAGES: :[[@LINE-1]]:24: warning: statement should be inside braces [readability-braces-around-statements]
+    handle(true);
+  else
+  // CHECK-MESSAGES: :[[@LINE-1]]:7: warning: statement should be inside braces [readability-braces-around-statements]
+    handle(false);
+}
+
+template <bool branch>
+void shouldPass() {
+  if constexpr (branch) {
+    handle(true);
+  } else {
+    handle(false);
+  }
+}
+
+void shouldFailNonTemplate() {
+  constexpr bool branch = false;
+  if constexpr (branch)
+  // CHECK-MESSAGES: :[[@LINE-1]]:24: warning: statement should be inside braces [readability-braces-around-statements]
+    handle(true);
+  else
+  // CHECK-MESSAGES: :[[@LINE-1]]:7: warning: statement should be inside braces [readability-braces-around-statements]
+    handle(false);
+}
+
+void shouldPass() {
+  constexpr bool branch = false;
+  if constexpr (branch) {
+    handle(true);
+  } else {
+    handle(false);
+  }
+}
+
+void run() {
+    shouldFail<true>();
+    shouldFail<false>();
+    shouldPass<true>();
+    shouldPass<false>();
+}