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I am trying diligently to network with other lawyers in my target region in order to land a position for next year. The problem is I am in a different geographical area for my 1L summer position, and I don't have a way to reasonably travel to these cities to grab a "cup of coffee" or to do lunch. Is it possible to network and form a connection with these lawyers through email/ over the phone? If so, how?

Yes, phone is totally fine and quite normal. Email first, introduce yourself and ask to set up a call at a mutually convenient time. Have a normal convo and get to know them/ask any questions you may have. Follow up occasionally with an email to update them on your progress/to just say hi. Finally, if you're ever in town, let them know and ask to meet for a coffee or lunch.

ETA: Some folks, as you alluded to on your post, start right off the bat by asking to meet in person. Although it sometimes works, it can more often be awkward/off-putting. This is just like anything else in life -- folks aren't necessarily keen on meeting with someone they've never even spoken to before.

So long and thanks for all the fish. If you decide you've had enough of the post-apocalyptic wasteland, feel free to join me over at TLS - with 100% fewer Lawcrossing articles.