If you anticipate being higher in cost than your competition, your proposal should justify the value in your bid. If possible, you should quantify that value. For example, if you have a higher up-front cost but offer lower long-term total cost of ownership, you should show how much you will save the customer in the long run. In Federal Government contracting, the evaluators specifically look for "Best Value" and may consider awarding to a higher priced bid if they can substantiate why it represents a better value. If you are worried about being undercut in price, then emphasize risk and continuity of service. Again, it is important to quantify things. Show the customer what an interruption in service can cost. If a lower cost means lower capacity or longer delivery time, show how the customer will be impacted. If a lower cost means lower quality, then demonstrate the cost of defects. The costs don't necessary have to be in dollars. For example, a delay might not have a dollar cost, but the customer will be negatively impacted. Show the down-side to every trade-off decision that can result in a lower cost. Position yourself as the low cost provider, because anything lower is simply unrealistic and not worth the risk. Show that you are cost conscious and how you have a lean, mean, and highly productive solution that is worth it because it represents the best value to the customer.
If you anticipate being lower in cost than you competition, you need to defend against the higher costs justifications above. Steal their themes. Demonstrate how your bid is the best value. Describe in detail how you've mitigated the risks. Provide a credible story for how you will ensure the customer is not negatively impacted. If there are trade-off decisions, show that the ones you made represent the best value. Show that you've provided the right amount of capacity, capability, and quality without building in any unnecessary costs. Show that there are added benefits to the customer of having an efficient solution. Turn things around and show how you can be quicker and more responsive because you've built in less fat.
If you are not sure whether you will be high or low, you have to assume that you will be high. But as you can see in both examples above, the key is value and how you show it. If you think you are probably in-between the highest and lowest costs, then you can position yourself as the best trade-off --- you have the lowest possible costs without making high-risk sacrifices. People often make this claim, but for it to be credible, you have to show the risks and how you've mitigated them.