Leonardo: disable TX- and RX-LED
Reading the answer from Gerben I realised the core of the issue: The TX/RX LED's on the Leonardo are wired PIN-LED-5V(common anode), whereas on the Olimexino-32U4 they are wired PIN-LED-GND(common cathode). So the two boards will need inverse signals for the same visual output.

Compare:
http://arduino.cc/en/uploads/Main/arduino-leonardo-schematic_3b.pdf
https://www.olimex.com/Products/Duino/AVR/OLIMEXINO-32U4/resources/OLIMEXINO-32U4_rev_A3.pdf



The most elegant solution will be to add a new board type (the code below is for IDE 1.0.x):


In your sketchbook create a folder 'hardware' and inside that 'olimexino'. In the olimexino folder create a file boards.txt with this content:

olimexino32u4.name=Olimexino-32U4
olimexino32u4.upload.protocol=avr109
olimexino32u4.upload.maximum_size=28672
olimexino32u4.upload.speed=57600
olimexino32u4.upload.disable_flushing=true
olimexino32u4.bootloader.low_fuses=0xff
olimexino32u4.bootloader.high_fuses=0xd8
olimexino32u4.bootloader.extended_fuses=0xcb
olimexino32u4.bootloader.path=caterina
olimexino32u4.bootloader.file=Caterina-Leonardo.hex
olimexino32u4.bootloader.unlock_bits=0x3F
olimexino32u4.bootloader.lock_bits=0x2F
olimexino32u4.build.mcu=atmega32u4
olimexino32u4.build.f_cpu=16000000L
olimexino32u4.build.vid=0x2341
olimexino32u4.build.pid=0x8036
olimexino32u4.build.core=arduino:arduino
olimexino32u4.build.variant=olimexino32u4

Create another folder 'variants' inside the olimexino folder.
Inside that, create the folder 'olimexino32u4'.
Now copy 'arduino/hardware/arduino/variants/leonardo/pins_arduino.h' to that folder
Open the copy for editing - the path should be 'sketchbook/hardware/olimexino/variants/olimexino32u4/pins_arduino.h'.
Change the section that deals with TXLED and RXLED by swapping the macros that end in 1 with those that end in 0. It should look like this:

#define TX_RX_LED_INIT  DDRD |= (1&lt;&lt;5), DDRB |= (1&lt;&lt;0)
#define TXLED1          PORTD |= (1&lt;&lt;5)
#define TXLED0          PORTD &amp;= ~(1&lt;&lt;5)
#define RXLED1          PORTB |= (1&lt;&lt;0)
#define RXLED0          PORTB &amp;= ~(1&lt;&lt;0)



I don't own the board so I can't test the solution. I hope that it solves your problem - just choose 'Olimexino-32U4' from the Tools->Board menu.