I assure you it works fine on Windows.
I am happy to hear that it works for you.
I just unpacked it, did "qmake" at the directory root, and then "qmake" at ./examples/qespta.
Here is a small part of the errors, I had to expand the WinXP Command Tool to 2000 lines:
C:\Documents and Settings\bnilsson\My Documents\Qt\qextserialport\examples\qespta>make
make -f Makefile.Debug
make[1]: Entering directory `C:/Documents and Settings/bnilsson/My Documents/Qt/qextserialport/examp
les/qespta'
g++ -enable-stdcall-fixup -Wl,-enable-auto-import -Wl,-enable-runtime-pseudo-reloc -mthreads -Wl -Wl
,-subsystem,windows -o debug\qespta.exe obj/main.o obj/MainWindow.o obj/MessageWindow.o obj/QespTest
.o obj/moc_MainWindow.o obj/moc_MessageWindow.o obj/moc_QespTest.o -L"..\..\build" -L"c:\Qt\4.4.0\l
ib" -lmingw32 -lqtmaind -lqextserialport -lQtGuid -lgdi32 -lcomdlg32 -loleaut32 -limm32 -lwinmm -lwi
nspool -lmsimg32 -lQtCored -lkernel32 -luser32 -lshell32 -luuid -lole32 -ladvapi32 -lws2_32
obj/main.o(.text+0x161): In function `Z5qMainiPPc':
C:/Documents and Settings/bnilsson/My Documents/Qt/qextserialport/examples/qespta/main.cpp:19: undef
ined reference to `_imp___ZN12QApplicationC1ERiPPci'
obj/main.o(.text+0x179):C:/Documents and Settings/bnilsson/My Documents/Qt/qextserialport/examples/q
espta/main.cpp:21: undefined reference to `_imp___Z18qInstallMsgHandlerPFv9QtMsgTypePKcE'
obj/main.o(.text+0x217):C:/Documents and Settings/bnilsson/My Documents/Qt/qextserialport/examples/q
espta/main.cpp:25: undefined reference to `_imp___ZN12QApplication4execEv'
obj/main.o(.text$_ZN10MainWindowD1Ev[MainWindow::~MainWindow()]+0x22): In function `ZN7QStringC1EPKc
':
c:/Qt/4.4.0/include/QtCore/../../src/corelib/arch/qatomic_windows.h: undefined reference to `_imp___
ZN11QMainWindowD2Ev'
I guess this has nothing to do with the serial port code, it looks like it does not link to Qt itself(?)
I have other Qt projects that works, so my installation seems to be ok.

Here is the .pro file:

################################################## ####################
# QextSerialPort Test Application (QESPTA)
################################################## ####################


PROJECT = QESPTA
TEMPLATE = app
DEPENDPATH += .
INCLUDEPATH += ../..
QMAKE_LIBDIR += ../../build


OBJECTS_DIR = obj
MOC_DIR = moc
UI_DIR = uic
CONFIG += qt thread warn_on


HEADERS += MainWindow.h \
MessageWindow.h \
QespTest.h

SOURCES += main.cpp \
MainWindow.cpp \
MessageWindow.cpp \
QespTest.cpp

LIBS += -lqextserialport

unixEFINES = _TTY_POSIX_
win32EFINES = _TTY_WIN_ QWT_DLL QT_DLL
I know this is not your stuff, but it will probably take longer for me to contact the authors themselves, and you may have a simple solution.
It will be essential for me to have access to a working example.

Thanks,

BN