There are alternatives to Experimental and Quasi-Experimental Impact Evaluation Methods.

Some of my clients are really interested in measuring their impact. RCTs and other quasi-experiments are first on their list of suggested designs. But our repertoire of IE designs and methods have grown.

This DfID working paper says:

Most development interventions are ‘contributory causes’. They ‘work’ as part of a causal package in combination with other ‘helping factors’ such as stakeholder behaviour, related programmes and policies, institutional capacities, cultural factors or socio-economic trends. Designs and methods for IE need to be able to unpick these causal packages. 
Demonstrating that interventions cause development effects depends on theories and rules of causal inference that can support causal claims. Some of the most potentially useful approaches to causal inference are not generally known or applied in the evaluation of international development and aid. Multiple causality and configurations; and theory-based evaluation that can analyse causal mechanisms are particularly weak. There is greater understanding of counterfactual logics, the approach to causal inference that underpins experimental approaches to IE. 

Methods that I am currently interested in include 

Qualitative Impact Assessment Protocol 

The QuIP gathers evidence of a project’s impact through narrative causal statements collected directly from intended project beneficiaries. Respondents are asked to talk about the main changes in their lives over a pre-defined recall period and prompted to share what they perceive to be the main drivers of these changes, and to whom or what they attribute any change - which may well be from multiple sources.
Typically, a QuIP study involves 24 semi-structured interviews and four focus groups, conducted in the native language by highly-skilled, local researchers. However, this number is not fixed and will depend on the sampling approach used. The research team conducting interviews are independent and blindfolded where appropriate; they are not aware who has commissioned the research or which project is being assessed. This helps to mitigate and reduce pro-project and confirmation bias, as well as enable a broader and more open discussion with respondents about all outcomes and drivers of change.

Qualitative Comparative Analysis 

Qualitative Comparative Analysis (QCA) is a means of analysing the causal contribution of different conditions (e.g. aspects of an intervention and the wider context) to an outcome of interest. QCA starts with the documentation of the different configurations of conditions associated with each case of an observed outcome. These are then subject to a minimisation procedure that identifies the simplest set of conditions that can account all the observed outcomes, as well as their absence. The results are typically expressed in statements expressed in ordinary language or as Boolean algebra. QCA is able to use relatively small and simple data sets. There is no requirement to have enough cases to achieve statistical significance, although ideally there should be enough cases to potentially exhibit all the possible configurations.