When your opponent actively blocks your shot they are usually right in front of you, you are within range and have a sense of where they are. They have also used one of their weapons (arm/hand) to block yours, sometimes they will use both weapons as in the case where your opponent shuts down the middle with both arms to block an uppercut. In this contact range there are a number predictable counters which are relatively easy to see and feel if you have enough experience. The only thing that kills predictability is speed, just watch how many times Winky Wright picked off Trinidad with the jab if you want to see an example of that.
If you want to be a good elusive boxer who can set up compound attacks and anticipate counters, you need an instinct for what to do when you miss a punch. The solution is very straightforward; As soon as you miss a punch, move your head.
If it’s a jab that you miss you will slip left or right while keeping your eye on your opponent, then jab again as you close the distance. If he starts firing a full combo then its probably best to go on the defensive or keep moving your head until he’s done and then come through. Most often when you miss it means your opponent has anticipated your move and is a half beat ahead of you, that’s all the time he needs to hit you with a clean shot. Developing an instinct for moving your head after you miss takes time, it will become second nature through sparring and hard lessons in the gym. Every now and then you will miss not because of the skill of your opponent but simply because you miscalculated or were off balance, either way the sames rules apply.
Start to get a good feel for when you land or miss in sparring so that you don’t just barge ahead with combos that leave you exposed after the first punch. You need sets of combos that can be adjusted and changed in mid flight. As well, in order for the instinct to become a technique you obviously need the right way of moving, and this comes from hours on the heavy bag of jabbing and slipping, slipping then jabbing, hooking and rolling/ducking and vice versa.
When you miss that shot your opponent is outside of your range, he could be left, right, or a bit too far in front of you. It doesn’t mean that you have to abandon your plan, it means that you lost a beat, you lost a step, and moving your head while adjusting to your opponent is the best way to gain that step back and re-initiate. Just as an example, many times you will miss the first jab you throw, guys are ready for it and they either step back or lean back, and if they are good they’ll throw a counter shot right away (often a left hook). In this case your staple combo will be – jab, slip, jab, jab, right.
Keep this in mind, apply it to your training, and come up with your own variations.