Did Justin Martyr and Marcion of Sinope have any contact with one another? I'm interested to discover if there is any evidence that Justin Martyr and Marcion of Sinope had any direct or indirect contact before Marcion left the Church. 

I suspect that they may have had indirect contact through writing because they were both influential and outspoken members of a relatively small educated Christian community around the same time – Marcion was 15 years older than Justin. Also, while Justin established himself in Rome, it is well known that Irenaeus of Gaul was heavily influenced by Justin's work and published his own writings only 15 years after Justin, so I suspect that Justin's work was widespread during his lifetime, perhaps early enough to be considered by Marcion. 

These suspicions, however, are weakened by the fact that I do not know when Justin became widely known or when Marcion left the church. Is there any evidence that Marcion read any of Justin's works, or that the two communicated in any way, either directly or indirectly?
Joseph B. Tyson (Marcion and Luke-Acts, page 24) says that almost everything we know about Marcion comes from polemics written by heresiologists in the second to fourth centuries, particularly Irenaeus. Neither Marcion nor Justin Martyr has left any extant writings that could connect the two in any meaningful way. 

Irenaeus (Against Heresies, iv.6) mentions a book by Justin Martyr 'Against Marcion', but this fragment scarcely suggests contact - in fact the reference to 'Against Marcion' suggests estrangement. Justin Martyr's First Apology, chapters 26,58 are also polemics against Marcion. Tyson points out (ibid, page 29) that in the First Apology, written about 150 CE, Martyr expresses no knowledge of Marcion's activities in Rome nor about his excommunication from the church there, saying that what is striking is that Justin Martyr is surprised that Marcion is still teaching. All this points to Martyr's knowledge of Marcion to be by reputation, rather than personal contact.

The estimated range of dating for the works of Justin Martyr is 150-160 CE, which would mean they were written towards the end of Marcion's lifetime. Whether any of these reached Marcion and whether he chose to read them is unknown. It is reasonable to assume they had no personal contact, either directly or indirectly.