Reader Question - What should I do about posterior leg pain during/after running?

Hard to say without doing an assessment. Could be a muscle strain or a nerve impingement. If pain or discomfort persists at rest for more than a week or two, Id suggest going to see a PT or Orthopedic Specialist. Better to address it immediately, than have it persist for weeks into your training schedule.
Your Sciatic nerve is the largest nerve in your body, running from the lower vertebrae to the feet,  and prone to compression at several spots. Signs and symptoms vary, ranging from sharp to dull pain in the lower back to burning, numbness, or tingling down the legs and into the foot.  If the compression originates in your lumbar vertebrae, you ll just have to wait for the irritation to cool off. Treatment involves rest, followed by glute, hamstring, and core strengthening exercises. I suggest trying some glute bridges, front and side planks if pain free. Begin with 3 sets of 15 for the bridges, and 3 sets of :20-:60 for the planks, until symptom free and then progress back into your lower body strength training exercises.
Sometimes, the Piriformis, a little muscle underneath the glute, becomes tight and or overactive, and can compress the nerve. Foam rolling your lower body, and adding these stretches may also help alleviate symptoms.  Running in the absence of strength training, can create instability and weakness  in the core, hips, and legs. Its a repetitive, quad dominant activity that can lead to muscular imbalances, if not balanced out with strength training, especially the posterior chain, and soft tissue work with a foam roller, and stretching. Give it a rest and then try the following foam rolling and strength training exercises several times per week, especially before runs, and the stretches several days a week, especially after runs.
 Foam Roll each area for :30-:60 seconds, focusing on tender spots. Follow immediately with glute and core activation work. Stop if symptoms persist.

 
Glutes

Glute Activation - 3 sets of 10-15 repetitions

Glute Bridge Finish
 
Lateral Band Walk - Glute Med

Core Activation - Hold for 3 sets of :20-:60 seconds

 
Side Plank

Pirifomis stretch - Lying supine on the floor, grab your right knee with left hand, and gently pull across your midline and towards your opposite shoulder, until a mild stretch is outer hip/glute. Breathe and hold for :30-:60 seconds, 2-4 sets on both sides. Stop if symptoms are present.

Glute/external rotator stretch - Bend your left knee and place your left foot on the floor, cross your right foot over your left knee. Reach through and grab the back on your left thigh, and gently pull your leg into your chest until you feel a light stretch. Relax your head and shoulders while you take a few deep breaths for a count of :30-:60 seconds, 2-4 sets on both sides. Stop if symptoms are present.

 

For more information please see my pages on foam rolling, glute and core activation

Low Trap Pulls for Increased Stability and Strength

Often when we look at shoulder stability, we focus on the scapulae retractors, the postural muscles that pull and squeeze the shoulder blades together, for greater stability during pushing and pulling movements. However, an often neglected aspect of scapulothoracic and glenohumeral rhythm involves the scapulae depressors as well. Not only is it important to squeeze and retract the shoulder blades together, but in order to create more space at the glenohumeral joint, thus decreasing impingement pathologies, the shoulder blades must rotate down and depress as well. Often these muscles are weak and or long, due to over active upper traps, and or overly kyphotic thoracic spines (poor posture). To improve both the length/tension relationship of your lower traps, and their strength, try a few of the following soft tissue, activation and strengthening exercises. You ll notice both increased strength in movements such as pull ups and the bench press, and you ll decrease your risk of achy or injured shoulders.

Begin with some soft tissue work at the thoracic spine. Lie on a foam roller. With your hands clasped behind your head or hugging opposing shoulders, gentle roll the upper 2/3 of your back. This exercise is great for loosening up the fascia around the thoracic spine (mid back), thus allowing for better mobility at the shoulder blade which should sit flush on your back, but is often protracted and rounded out, due to poor, kyphotic posture.

From there, foam roll your lats. Immediately after your SMR work, perform several reps of your favorite thoracic mobility drill, followed by an activation exercise like the one performed with a band in the video or the wall angels in the next video.

 

Wall Angels can be done against a wall or lying on the floor. Pulling your shoulder blades down and together, slowly flex your arms straight overhead, maintaining contact with the wall or floor throughout the movement. Focus on pulling the shoulder blades down and together as you lower your arms.

 

After your done a few minutes of soft tissue and activation work. Perform a low trap exercise like the one below. If you aren't strong enough to do them from a pull up bar, begin with a lat pull down machine, progressing the load to body weight. Make sure you are able to get a good symmetrical squeeze as you pull your shoulders down and away from your ears. Notice in this example as my client begins to fatigue, an asymmetry on his right side is more pronounced and uneven.