diff --git a/.travis.yml b/.travis.yml
index b3417019..94f75443 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,10 +1,8 @@
 language: cpp
 sudo: required
 dist: xenial
-osx_image: xcode10.1 # macOS 10.13
 os:
   - linux
-  - osx
 compiler:
   - gcc
   - clang
@@ -39,20 +37,32 @@ jobs:
       env: DOCKER_BUILD=ubuntu-18.04
     - os: linux
       env: DOCKER_BUILD=ubuntu-19.10
-  exclude:
-    # Various macOS tests seem to be broken.
+
+    # macOS tests
     - os: osx
-      compiler: gcc
+      osx_image: xcode10.1 # macOS 10.13
+      compiler: clang
+      env: LLVM_CONFIG=llvm-config-3.5 CLANG=clang-3.5
     - os: osx
-      env: LLVM_CONFIG=llvm-config-5.0 CLANG=clang-5.0 USE_CMAKE=1
+      osx_image: xcode10.1 # macOS 10.13
+      compiler: clang
+      env: LLVM_CONFIG=llvm-config-3.8 CLANG=clang-3.8
     - os: osx
-      env: LLVM_CONFIG=llvm-config-6.0 CLANG=clang-6.0 USE_CMAKE=1 STATIC_LLVM=0 STATIC_LUAJIT=0
+      osx_image: xcode11.3 # macOS 10.14
+      compiler: clang
+      env: LLVM_CONFIG=llvm-config-6.0 CLANG=clang-6.0 USE_CMAKE=1
     - os: osx
-      env: LLVM_CONFIG=llvm-config-8 CLANG=clang-8
+      osx_image: xcode11.3 # macOS 10.14
+      compiler: clang
+      env: LLVM_CONFIG=llvm-config-7 CLANG=clang-7 USE_CMAKE=1
     - os: osx
-      env: LLVM_CONFIG=llvm-config-9 CLANG=clang-9
+      osx_image: xcode11.3 # macOS 10.14
+      compiler: clang
+      env: LLVM_CONFIG=llvm-config-8 CLANG=clang-8 USE_CMAKE=1
     - os: osx
-      env: LLVM_CONFIG=llvm-config-9 CLANG=clang-9 USE_CMAKE=1 STATIC_LLVM=0 STATIC_LUAJIT=0
+      osx_image: xcode11.3 # macOS 10.14
+      compiler: clang
+      env: LLVM_CONFIG=llvm-config-9 CLANG=clang-9 USE_CMAKE=1
 
 script:
   - ./travis.sh
diff --git a/Makefile b/Makefile
index 4689b16e..336e6a82 100644
--- a/Makefile
+++ b/Makefile
@@ -209,7 +209,8 @@ endif
 build/lib/libluajit-5.1.a: build/$(LUAJIT_TAR)
 	(cd build; tar -xf $(LUAJIT_TAR))
 	# MACOSX_DEPLOYMENT_TARGET is a workaround for https://github.com/LuaJIT/LuaJIT/issues/484
-	(cd $(LUAJIT_DIR); $(MAKE) install PREFIX=$(realpath build) CC=$(CC) STATIC_CC="$(CC) -fPIC" MACOSX_DEPLOYMENT_TARGET=10.6)
+	# see also https://github.com/LuaJIT/LuaJIT/issues/575
+	(cd $(LUAJIT_DIR); $(MAKE) install PREFIX=$(realpath build) CC=$(CC) STATIC_CC="$(CC) -fPIC" MACOSX_DEPLOYMENT_TARGET=10.7)
 
 release/include/terra/%.h:  $(LUAJIT_INCLUDE)/%.h $(LUAJIT_LIB) 
 	cp $(LUAJIT_INCLUDE)/$*.h $@
diff --git a/cmake/Modules/GetLuaJIT.cmake b/cmake/Modules/GetLuaJIT.cmake
index 328a8cb1..d0348a5a 100644
--- a/cmake/Modules/GetLuaJIT.cmake
+++ b/cmake/Modules/GetLuaJIT.cmake
@@ -104,7 +104,8 @@ else()
     OUTPUT ${LUAJIT_STATIC_LIBRARY} ${LUAJIT_SHARED_LIBRARY_PATHS} ${LUAJIT_EXECUTABLE} ${LUAJIT_INSTALL_HEADERS}
     DEPENDS ${LUAJIT_SOURCE_DIR}
     # MACOSX_DEPLOYMENT_TARGET is a workaround for https://github.com/LuaJIT/LuaJIT/issues/484
-    COMMAND make install "PREFIX=${LUAJIT_INSTALL_PREFIX}" "CC=${CMAKE_C_COMPILER}" "STATIC_CC=${CMAKE_C_COMPILER} -fPIC" MACOSX_DEPLOYMENT_TARGET=10.6
+    # see also https://github.com/LuaJIT/LuaJIT/issues/575
+    COMMAND make install "PREFIX=${LUAJIT_INSTALL_PREFIX}" "CC=${CMAKE_C_COMPILER}" "STATIC_CC=${CMAKE_C_COMPILER} -fPIC" MACOSX_DEPLOYMENT_TARGET=10.7
     WORKING_DIRECTORY ${LUAJIT_SOURCE_DIR}
     VERBATIM
   )
diff --git a/tests/dynlib.t b/tests/dynlib.t
index 09e725bd..3b106ebf 100644
--- a/tests/dynlib.t
+++ b/tests/dynlib.t
@@ -1,7 +1,7 @@
 local ffi = require 'ffi'
 -- test that the dynamic library for terra was built correctly
 -- by compiling a new program that links against it and running it
-terralib.includepath = terralib.terrahome.."/include/terra"
+terralib.includepath = terralib.includepath .. ";" .. terralib.terrahome .. "/include/terra"
 C = terralib.includecstring [[
 #include <stdio.h>
 #include "terra.h"
diff --git a/tests/exportdynamic.t b/tests/exportdynamic.t
index 3bbd63b3..0583823f 100644
--- a/tests/exportdynamic.t
+++ b/tests/exportdynamic.t
@@ -1,4 +1,4 @@
-terralib.includepath = terralib.terrahome.."/include/terra"
+terralib.includepath = terralib.includepath .. ";" .. terralib.terrahome .. "/include/terra"
 C = terralib.includecstring [[
     #include "lua.h"
     #include "lauxlib.h"
diff --git a/tests/lib/objc.t b/tests/lib/objc.t
index c3758645..82e476be 100644
--- a/tests/lib/objc.t
+++ b/tests/lib/objc.t
@@ -14,13 +14,18 @@ local mangleSelector
 --replace methods such as:   myobj:methodcall(arg0,arg1)
 --with calls to the objc runtime api: objc_msgSend(&obj,sel_registerName("methodcall"),arg0,arg1) 
 
+-- Hack: As of macOS 10.15 this type signature has changed, see:
+-- https://www.mikeash.com/pyblog/objc_msgsends-new-prototype.html
+local objc_msgSend_type = terralib.types.funcpointer(
+  {&C.objc_object, &C.objc_selector}, &C.objc_object, true)
+
 local struct Wrapper {
     data : &C.objc_object
 }
 Wrapper.metamethods.__methodmissing = macro(function(sel,obj,...)
 	local arguments = {...}
 	sel = mangleSelector(sel,#arguments)
-	return `Wrapper { C.objc_msgSend(obj.data,C.sel_registerName(sel),arguments) }
+	return `Wrapper { ([objc_msgSend_type](C.objc_msgSend))(obj.data,C.sel_registerName(sel),arguments) }
 end)
 
 function mangleSelector(sel,nargs)
diff --git a/tests/luaapi.t b/tests/luaapi.t
index 10a69360..f615d427 100644
--- a/tests/luaapi.t
+++ b/tests/luaapi.t
@@ -1,4 +1,4 @@
-terralib.includepath = terralib.terrahome.."/include/terra"
+terralib.includepath = terralib.includepath .. ";" .. terralib.terrahome .. "/include/terra"
 C = terralib.includecstring [[
     #include "lua.h"
     #include "lauxlib.h"
diff --git a/travis.sh b/travis.sh
index 5d5350fc..2a5cd83e 100755
--- a/travis.sh
+++ b/travis.sh
@@ -142,6 +142,11 @@ if [[ $(uname) = Darwin ]]; then
     hdiutil detach /Volumes/CUDAMacOSXInstaller
   fi
 
+  # workaround for https://github.com/terralang/terra/issues/365
+  if [[ ! -e /usr/include ]]; then
+    export INCLUDE_PATH="$(xcrun --sdk macosx --show-sdk-path)/usr/include"
+  fi
+
   export PATH=$PWD:$PATH
 fi
 
@@ -167,16 +172,28 @@ if [[ $USE_CMAKE -eq 1 ]]; then
       -DTERRA_SLIB_INCLUDE_LUAJIT=OFF
     )
   fi
+  if [[ $(uname) = Darwin ]]; then
+    # Hack: CMake tries to be smart and use XCode's copy of Clang by
+    # default. This causes LuaJIT to not build on Mojave and later
+    # (math.h not found) if the header package is not installed.
+    CMAKE_FLAGS+=(
+      -DCMAKE_C_COMPILER=$(which $CC)
+      -DCMAKE_CXX_COMPILER=$(which $CXX)
+    )
+  fi
 
   pushd build
   cmake .. -DCMAKE_INSTALL_PREFIX=$PWD/../install "${CMAKE_FLAGS[@]}"
   make install -j2
-  ctest -j2 || (test "$(uname)" = "Darwin" && test "$LLVM_CONFIG" = "llvm-config-3.8")
+  ctest --output-on-failure -j2 || (test "$(uname)" = "Darwin" && test "$LLVM_CONFIG" = "llvm-config-3.8")
   popd
 
-  pushd tests
-  ../install/bin/terra ./run
-  popd
+  # Skip this on macOS because it spews too much on Mojave and newer.
+  if [[ $(uname) != Darwin ]]; then
+      pushd tests
+      ../install/bin/terra ./run
+      popd
+  fi
 else
   make LLVM_CONFIG=$(which $LLVM_CONFIG) CLANG=$(which $CLANG) test