I'm going to assume you are working with SQL Server 2008 or newer, which is required to make the dense_rank() function work. 
The solution below goes through a few steps that are outlined in the comments. One call out is that I changed one of the @ProductRecipe records from (22, 130) to (22, 468) as I believe it to be the intended sample data because Component1 of the desired output includes PricingID values 316323 and 316329.
Answer:
DECLARE @ProductRecipe TABLE (ProductRecipeID INT, ComponentProductID INT)
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (21, 130)
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (21, 468)
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (21, 500)
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (22, 468) --values were (22, 130) in question
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (22, 500)
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (23, 130)
INSERT INTO @ProductRecipe (ProductRecipeID, ComponentProductID) VALUES (23, 501)
DECLARE @ComponentPricing TABLE (PricingID INT, ProductID INT)
INSERT INTO @ComponentPricing (PricingID, ProductID)
VALUES (314023, 130)
 , (313616, 130)
 , (313071, 130)
 , (312865, 130)
 , (316323, 468)
 , (316329, 468)
 , (398864, 500)
; with base as
    (
        --Joining the two datasets together.
        select pr.ProductRecipeID
        , pr.ComponentProductID
        , cp.PricingID
        from @ProductRecipe as pr
        left join @ComponentPricing as cp on pr.ComponentProductID = cp.ProductID   
    )
    , pr_exclude as
    (
        --Identifying that ProductRecipeID 23 should be excluded because of the 501 NULL value
        select distinct b.ProductRecipeID
        from base as b
        where b.PricingID is null   
    )
    , final_base as
    (
        --Assigning Rank to each ComponentProductID
        select b.ProductRecipeID
        , b.ComponentProductID
        , b.PricingID
        , dense_rank() over (partition by b.ProductRecipeID order by b.ComponentProductID asc) as prod_rnk
        from base as b
        left join pr_exclude as p on b.ProductRecipeID = p.ProductRecipeID
        where 1=1
        and p.ProductRecipeID is null
    )
--Joining it all together
select a.ProductRecipeID
, a.PricingID as Component1
, b.PricingID as Component2
, c.PricingID as Component3
, d.PricingID as Component4
, e.PricingID as Component5
from final_base as a
left join final_base as b on a.ProductRecipeID = b.ProductRecipeID and b.prod_rnk = 2
left join final_base as c on b.ProductRecipeID = c.ProductRecipeID and c.prod_rnk = 3
left join final_base as d on c.ProductRecipeID = d.ProductRecipeID and d.prod_rnk = 4
left join final_base as e on d.ProductRecipeID = e.ProductRecipeID and e.prod_rnk = 5
where a.prod_rnk = 1
order by 1, 2, 3, 4, 5, 6